These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.
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Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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Johannes Nokkala et al 2024 J. Phys. A: Math. Theor. 57 233001
Géza Tóth and Iagoba Apellaniz 2014 J. Phys. A: Math. Theor. 47 424006
We summarize important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with Greenberger–Horne–Zeilinger states, Dicke states and singlet states. We calculate the highest precision achievable in these schemes. Then, we present the fundamental notions of quantum metrology, such as shot-noise scaling, Heisenberg scaling, the quantum Fisher information and the Cramér–Rao bound. Using these, we demonstrate that entanglement is needed to surpass the shot-noise scaling in very general metrological tasks with a linear interferometer. We discuss some applications of the quantum Fisher information, such as how it can be used to obtain a criterion for a quantum state to be a macroscopic superposition. We show how it is related to the speed of a quantum evolution, and how it appears in the theory of the quantum Zeno effect. Finally, we explain how uncorrelated noise limits the highest achievable precision in very general metrological tasks.
This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
Jing Liu et al 2020 J. Phys. A: Math. Theor. 53 023001
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér–Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér–Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.
Giuseppe Gaeta and Epifanio G Virga 2023 J. Phys. A: Math. Theor. 56 363001
In its most restrictive definition, an octupolar tensor is a fully symmetric traceless third-rank tensor in three space dimensions. So great a body of works have been devoted to this specific class of tensors and their physical applications that a review would perhaps be welcome by a number of students. Here, we endeavour to place octupolar tensors into a broader perspective, considering non-vanishing traces and non-fully symmetric tensors as well. A number of general concepts are recalled and applied to either octupolar and higher-rank tensors. As a tool to navigate the diversity of scenarios we envision, we introduce the octupolar potential, a scalar-valued function which can easily be given an instructive geometrical representation. Physical applications are plenty; those to liquid crystal science play a major role here, as they were the original motivation for our interest in the topic of this review.
Luca Angelani 2023 J. Phys. A: Math. Theor. 56 455003
The motion of run-and-tumble particles in one-dimensional finite domains are analyzed in the presence of generic boundary conditions. These describe accumulation at walls, where particles can either be absorbed at a given rate, or tumble, with a rate that may be, in general, different from that in the bulk. This formulation allows us to treat in a unified way very different boundary conditions (fully and partially absorbing/reflecting, sticky, sticky-reactive and sticky-absorbing boundaries) which can be recovered as appropriate limits of the general case. We report the general expression of the mean exit time, valid for generic boundaries, discussing many case studies, from equal boundaries to more interesting cases of different boundary conditions at the two ends of the domain, resulting in nontrivial expressions of mean exit times.
Jacob C Bridgeman and Christopher T Chubb 2017 J. Phys. A: Math. Theor. 50 223001
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes.
These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states.
The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.
John Goold et al 2016 J. Phys. A: Math. Theor. 49 143001
This topical review article gives an overview of the interplay between quantum information theory and thermodynamics of quantum systems. We focus on several trending topics including the foundations of statistical mechanics, resource theories, entanglement in thermodynamic settings, fluctuation theorems and thermal machines. This is not a comprehensive review of the diverse field of quantum thermodynamics; rather, it is a convenient entry point for the thermo-curious information theorist. Furthermore this review should facilitate the unification and understanding of different interdisciplinary approaches emerging in research groups around the world.
Martin R Evans et al 2020 J. Phys. A: Math. Theor. 53 193001
In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field.
Vasileios A Letsios 2024 J. Phys. A: Math. Theor. 57 135401
In our previous article (Letsios 2023 J. High Energy Phys. JHEP05(2023)015), we showed that the strictly massless spin-3/2 field, as well as the strictly and partially massless spin-5/2 fields, on N-dimensional () de Sitter (dS) spacetime (dSN) are non-unitary unless N = 4. The (non-)unitarity was demonstrated by simply observing that there is a (mis-)match between the representation-theoretic labels that correspond to the unitary irreducible representations (UIR's) of the dS algebra spin and the ones corresponding to the space of eigenmodes of the field theories. In this paper, we provide a technical representation-theoretic explanation for this fact by studying the (non-)existence of positive-definite, dS invariant scalar products for the spin-3/2 and spin-5/2 strictly/partially massless eigenmodes on dSN (). Our basic tool is the examination of the action of spin generators on the space of eigenmodes, leading to the following findings. For odd N, any dS invariant scalar product is identically zero. For even N > 4, any dS invariant scalar product must be indefinite. This gives rise to positive-norm and negative-norm eigenmodes that mix with each other under spin boosts. In the N = 4 case, the positive-norm sector decouples from the negative-norm sector and each sector separately forms a UIR of spin(4, 1). Our analysis makes extensive use of the analytic continuation of tensor-spinor spherical harmonics on the N-sphere (SN) to dSN and also introduces representation-theoretic techniques that are absent from the mathematical physics literature on half-odd-integer-spin fields on dSN.
Iddo Eliazar 2024 J. Phys. A: Math. Theor. 57 225003
Brownian motion (BM) is the paradigmatic model of diffusion. Transcending from diffusion to anomalous diffusion, the principle Gaussian generalizations of BM are Scaled BM (SBM) and Fractional BM (FBM). In the sub/super diffusivity regimes: SBM is characterized by aging/anti-aging, and FBM is characterized by anti-persistence/persistence. BM is neither aging/anti-aging, nor persistent/anti-persistent. Within the realm of diffusion, a recent Gaussian generalization of BM, Weird BM (WBM), was shown to display aging/anti-aging and persistence/anti-persistence. This paper introduces and explores the anomalous-diffusion counterpart of WBM—termed Beta BM (BBM) due to its inherent beta-function kernel structure—and shows that: the weird behaviors of WBM become even weirder when elevating to BBM. Indeed, BBM displays a rich assortment of anomalous behaviors, and an even richer assortment of combinations of anomalous behaviors. In particular, the BBM anomalous behaviors include aging/anti-aging and persistence/anti-persistence—which BBM displays in both the sub and super diffusivity regimes. So, anomalous behaviors that are unattainable by the prominent models of SBM and FBM are well attainable by the BBM model.
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Yi Yang and Shuigeng Zhou 2024 J. Phys. A: Math. Theor. 57 258001
We present an algorithm to compute the exact critical probability h(n) for an helical square lattice with random and independent site occupancy. The algorithm has time complexity and space complexity with c = 2.7459... and allows us to compute h(n) up to n = 24. Since the extrapolation result of h(n) is inconsistent with the current best estimation of pc, we also compute and extend the exact critical probability for an cylindrical square lattice to n = 24. Our calculation shows that the current best result of by Jacobsen (2015 J. Phys. A: Math. Theor.48 454003) is incorrect and the corrected value should be .
Xiaoyan Wu et al 2024 J. Phys. A: Math. Theor. 57 255202
We develop lattice eigenfunction equations of the lattice KdV equation, which are equations obeyed by auxiliary functions, or eigenfunctions, of the Lax pair of the lattice KdV equation. These equations are three-dimensionally consistent quad-equations, that are closely related to lattice equations in the Adler-Bobenko-Suris (ABS) classification. The connection between the H3(δ), Q1(δ), Q2 and Q3(δ) equations in the ABS classification and the lattice eigenfunction equations is explicitly showed. In particular, we provide a natural interpretation of the δ term in those equations. This can be understood as 'interactions' between the eigenfunctions. Other integrable properties of the eigenfunction equations, such as exact solutions, discrete zero curvature conditions are also provided. We believe that the approach presented in this paper can be used as a means to search for integrable lattice equations.>
Jesper Lykke Jacobsen 2024 J. Phys. A: Math. Theor. 57 258002
The authors replies to the comment made by Yang and Zhou (2024 J. Phys. A: Math. Theor.) on his 2015 paper entitled 'Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras' (Jacobsen 2015 J. Phys. A: Math. Theor.48 454003).
Agung Budiyono et al 2024 J. Phys. A: Math. Theor. 57 255301
Just a few years after the inception of quantum mechanics, there has been a research program using the nonclassical values of some quasiprobability distributions to delineate the nonclassical aspects of quantum phenomena. In particular, in Kirkwood–Dirac (KD) quasiprobability distribution, the distinctive quantum mechanical feature of noncommutativity which underlies many nonclassical phenomena, manifests in the nonreal values and/or the negative values of the real part. Here, we develop a faithful quantifier of quantum coherence based on the KD nonclassicality which captures simultaneously the nonreality and the negativity of the KD quasiprobability. The KD-nonclassicality coherence thus defined, is upper bounded by the uncertainty of the outcomes of measurement described by a rank-1 orthogonal projection-valued measure (PVM) corresponding to the incoherent orthonormal basis which is quantified by the Tsallis -entropy. Moreover, they are identical for pure states so that the KD-nonclassicality coherence for pure state admits a simple closed expression in terms of measurement probabilities. We then use the Maassen–Uffink uncertainty relation for min-entropy and max-entropy to obtain a lower bound for the KD-nonclassicality coherence of a pure state in terms of optimal guessing probability in measurement described by a PVM noncommuting with the incoherent orthonormal basis. We also derive a trade-off relation for the KD-nonclassicality coherences of a pure state relative to a pair of noncommuting orthonormal bases with a state-independent lower bound. Finally, we sketch a variational scheme for a direct estimation of the KD-nonclassicality coherence based on weak value measurement and thereby discuss its relation with quantum contextuality.
Thomas Bothner and Alex Little 2024 J. Phys. A: Math. Theor. 57 255201
We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically given by a generalization of the Gaudin-Mehta distribution, in the limit of weak non-Hermiticity. The same generalization is expressed in terms of an integro-differential Painlevé function and it is shown that the generalized Gaudin-Mehta distribution describes the crossover, with increasing degree of non-Hermiticity, from Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex Ginibre Ensemble.
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Iddo Eliazar 2024 J. Phys. A: Math. Theor. 57 233002
Diffusion is a generic term for random motions whose positions become more and more diffuse with time. Diffusion is of major importance in numerous areas of science and engineering, and the research of diffusion is vast and profound. This paper is the first in a stochastic 'intro series' to the multidisciplinary field of diffusion. The paper sets off from a basic question: how to quantitatively measure diffusivity? Having answered the basic question, the paper carries on to a follow-up question regarding statistical behaviors of diffusion: what further knowledge can the diffusivity measure provide, and when can it do so? The answers to the follow-up question lead to an assortment of notions and topics including: persistence and anti-persistence; aging and anti-aging; short-range and long-range dependence; the Wiener–Khinchin theorem and its generalizations; spectral densities, white noise, and their generalizations; and colored noises. Observing diffusion from a macro level, the paper culminates with: the universal emergence of power-law diffusivity; the three universal diffusion regimes—one regular, and two anomalous; and the universal emergence of 1/f noise. The paper is entirely self-contained, and its prerequisites are undergraduate mathematics and statistics.
Johannes Nokkala et al 2024 J. Phys. A: Math. Theor. 57 233001
These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is flourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising field of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer significant complex network properties. The field features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that unifies the field of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.
Piotr Mironowicz 2024 J. Phys. A: Math. Theor. 57 163002
This paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations, optimize quantum states, and design efficient quantum algorithms and protocols. The paper also discusses implementational aspects, such as solvers for SDP and modeling tools, enabling the effective employment of optimization techniques in quantum information processing. The insights and methodologies presented in this paper have proven instrumental in advancing the field of quantum information, facilitating the development of novel communication protocols, self-testing methods, and a deeper understanding of quantum entanglement.
Manuel de León and Rubén Izquierdo-López 2024 J. Phys. A: Math. Theor. 57 163001
In this paper we study coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of coisotropic reduction is motivated by the fact that these dynamics can always be interpreted as Lagrangian or Legendrian submanifolds. Furthermore, Lagrangian or Legendrian submanifolds can be reduced by a coisotropic one.
J S Dehesa 2024 J. Phys. A: Math. Theor. 57 143001
Rydberg atoms and excitons are composed so that they have a hydrogenic energy level structure governed by the Rydberg formula. They are relevant per se and for their numerous applications, e.g. facilitating the creation of novel quantum devices in quantum technologies which are inherently robust, miniature, and scalable (basically because they exist in solid-state platforms) and the realization of synthetic dimensions in numerous quantum-mechanical systems, giving rise to quantum matter which can behave as if it were in dimensions other than three. However the quantification of their internal disorder is scarcely known. Here we show and review the knowledge of dispersion, entanglement, physical entropies (Rényi, Shannon) and complexity-like measures of D-dimensional Rydberg systems with in both position and momentum spaces. These uncertainty quantifiers are expressed in terms of D, the potential strength and the hyperquantum numbers of the Rydberg states. This has been possible because of the fine asymptotics of algebraic functionals the Laguerre and Gegenbauer polynomials which, together with the hyperspherical harmonics, control the Rydberg wavefunctions.
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Tim Adamo and Sumer Jaitly 2020 J. Phys. A: Math. Theor. 53 055401
Four-dimensional conformal fishnet theory is an integrable scalar theory which arises as a double scaling limit of -deformed maximally supersymmetric Yang–Mills. We give a perturbative reformulation of -deformed super-Yang–Mills theory in twistor space, and implement the double scaling limit to obtain a twistor description of conformal fishnet theory. The conformal fishnet theory retains an abelian gauge symmetry on twistor space which is absent in space-time, allowing us to obtain cohomological formulae for scattering amplitudes that manifest conformal invariance. We study various classes of scattering amplitudes in twistor space with this formalism.
Keith Alexander et al 2020 J. Phys. A: Math. Theor. 53 045001
We probe the character of knotting in open, confined polymers, assigning knot types to open curves by identifying their projections as virtual knots. In this sense, virtual knots are transitional, lying in between classical knot types, which are useful to classify the ambiguous nature of knotting in open curves. Modelling confined polymers using both lattice walks and ideal chains, we find an ensemble of random, tangled open curves whose knotting is not dominated by any single knot type, a behaviour we call weakly knotted. We compare cubically confined lattice walks and spherically confined ideal chains, finding the weak knotting probability in both families is quite similar and growing with length, despite the overall knotting probability being quite different. In contrast, the probability of weak knotting in unconfined walks is small at all lengths investigated. For spherically confined ideal chains, weak knotting is strongly correlated with the degree of confinement but is almost entirely independent of length. For ideal chains confined to tubes and slits, weak knotting is correlated with an adjusted degree of confinement, again with length having negligible effect.
Yongchao Lü and Joseph A Minahan 2020 J. Phys. A: Math. Theor. 53 024001
We consider anomaly cancellation for gauge theories where the left-handed chiral multiplets are in higher representations. In particular, if the left-handed quarks and leptons transform under the triplet representation of and if the gauge group is compact then up to an overall scaling there is only one possible nontrivial assignment for the hypercharges if N = 3, and two if N = 9. Otherwise there are infinitely many. We use the Mordell–Weil theorem, Mazur's theorem and the Cremona elliptic curve database which uses Kolyvagin's theorem on the Birch Swinnerton-Dyer conjecture to prove these statements.
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Barbero et al
The temporal evolution of the surface electric field in a cell in the presence of ionic adsorption is investigated. The analysis is performed in the framework of the Poisson-Nernst-Planck model, based on the conservation of particles and the equation of Poisson for the actual electric potential across the cell, assuming that only the ions of a given sign are mobile. The adsorption is described using a kinetic equation of Langmuir's type. The simple case of small adsorption is considered, in which the saturation effect can be neglected, and the fundamental equations of the model can be linearized. In this framework, the effective relaxation time describing the dynamics of the system is evaluated, as well as the profiles of the ions and the electric field. The case in which the sample is a half-space is first considered. A more realistic situation where the sample is a slab of thickness $d$, limited by two identical or different electrodes, is analyzed too. The difference in electric potential due to the adsorption phenomenon between the electrodes is determined. Our analysis shows that its time dependence, when the electrodes have different adsorption properties, is not monotonic.
Gong
A conceptual quantity---the minimal effective amount of a quantum state $\phi(\textbf{r}_j)$ in d-dimensional systems, defined by $N_{*}=\sum_{j=1}^N{\min\{N|\phi(\textbf{r}_j)|^2,1\}}$, is newly proposed, where system sizes $N=L^d$. The effective dimension $d_{IR}$ can be calculated by $N_{*}=h_{*}(L)L^{d_{IR}}$, where $h_{*}(L)$ doesn't change faster than any nonzero power. However, the nature of $h_{*}(L)$ is unknown priori in any given model, but is at the same time very important for its numerical analysis. Hence, analytical results can provide insights on $h_{*}(L)$ in more complex situations. In this paper, we get exact results of 1D continuous sine functions, exponential decay functions and power-law decay functions. They are used to distinguish extended and localized phases in the 1D uniform potential model, Anderson model and HMP (hopping rates modulated by a power-law function) model.
Cantarella et al
We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of Cantarella, Duplantier, Shonkwiler, and Uehara and has (expected) time per sample quadratic in the number of edges in the polygon. We use our new sampling method and a new code for computing invariants based on the Alexander polynomial to investigate the probability of finding unknots among equilateral closed polygons.
Frembs et al
The Choi-Jamiolkowski isomorphism is an essential component in every quantum information theorist's toolkit: it allows to identify linear maps between two quantum systems with linear operators on the composite system. Here, we analyse this widely used gadget from a new perspective. Namely, we explicitly distinguish between its kinematical and dynamical properties, that is, we study the isomorphism on two different levels: Jordan algebras and the different C∗-algebras they arise from, which are distinguished by their order of composition.
A number of important and novel insights stem from our analysis. We find that Choi's theorem, which asserts that Choi's version of the isomorphism [M.-D. Choi, Lin. Alg. Appl., 10, 285 (1975)] further maps the positive cone of completely positive linear maps (such as quantum channels) to the cone of positive linear operators (such as quantum states) on the composite system, crucially
depends on the dynamical (compositional) structure in C∗-algebras. This in turn lies at the heart of the mismatch between the basis-dependence of Choi's version of the isomorphism, and the basis-independent version by Jamiolkowski [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. Here, we overcome this subtle but pervasive issue in a number of ways: first, we prove a version
of Choi's theorem for Jamiolkowski's isomorphism, second, we define a basis-independent variant of Choi's isomorphism and, third, by making explicit the dynamical distinction between Jordan and C∗-algebras, we combine the different variants of the isomorphism into a unified description, that subsumes their individual features. We also embed and interpret our results in the graphical calculus of categorical quantum mechanics.
Castro-Alvaredo et al
In recent years a considerable amount of attention has been devoted to the investigation of 2D quantum field theories perturbed by certain types of irrelevant operators. These are the composite field $\TTb$ -- constructed out of the components of the stress-energy tensor -- and its generalisations -- built from higher-spin conserved currents.
The effect of such perturbations on the infrared and ultraviolet properties of the theory has been extensively investigated.
 In the context of integrable quantum field theories, a fruitful perspective is that of factorised scattering theory. In fact, the above perturbations were shown to preserve integrability. The resulting deformed scattering matrices -- extensively analysed with the thermodynamic Bethe ansatz -- provide the first step in the development of a bootstrap program.
In this paper we present a systematic approach to computing matrix elements of operators in generalised $\TTb$-perturbed models, based on employing the standard form factor program. We show that for theories with diagonal scattering and certain types of fields the deformed form factors, factorise into the product of the undeformed ones and of a perturbation- and theory-dependent term.
From these solutions, correlation functions can be obtained and their asymptotic properties studied.
Trending on Altmetric
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Thomas Bothner and Alex Little 2024 J. Phys. A: Math. Theor. 57 255201
We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically given by a generalization of the Gaudin-Mehta distribution, in the limit of weak non-Hermiticity. The same generalization is expressed in terms of an integro-differential Painlevé function and it is shown that the generalized Gaudin-Mehta distribution describes the crossover, with increasing degree of non-Hermiticity, from Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex Ginibre Ensemble.
E A Bergshoeff et al 2024 J. Phys. A: Math. Theor. 57 245205
We study D-dimensional p-brane Galilean geometries via the intrinsic torsion of the adapted connections of their degenerate metric structure. These non-Lorentzian geometries are examples of G-structures whose characteristic tensors consist of two degenerate 'metrics' of ranks and . We carry out the analysis in two different ways. In one way, inspired by Cartan geometry, we analyse in detail the space of intrinsic torsions (technically, the cokernel of a Spencer differential) as a representation of G, exhibiting for generic (p, D) five classes of such geometries, which we then proceed to interpret geometrically. We show how to re-interpret this classification in terms of ()-brane Carrollian geometries. The same result is recovered by methods inspired by similar results in the physics literature: namely by studying how far an adapted connection can be determined by the characteristic tensors and by studying which components of the torsion tensor do not depend on the connection. As an application, we derive a gravity theory with underlying p-brane Galilean geometry as a non-relativistic limit of Einstein–Hilbert gravity and discuss how it gives a gravitational realisation of some of the intrinsic torsion constraints found in this paper. Our results also have implications for gravity theories with an underlying ()-brane Carrollian geometry.
Luca Fabbri 2024 J. Phys. A: Math. Theor. 57 245204
We employ the polar re-formulation of spinor fields to see in a new light their classification into regular and singular spinors, these last also called flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles: in particular, we will study the conditions under which flagpoles may be solutions of the Dirac field equations. We argue for an enlargement of the plane-wave expansion.
Giovanni Barbero et al 2024 J. Phys. A: Math. Theor.
The temporal evolution of the surface electric field in a cell in the presence of ionic adsorption is investigated. The analysis is performed in the framework of the Poisson-Nernst-Planck model, based on the conservation of particles and the equation of Poisson for the actual electric potential across the cell, assuming that only the ions of a given sign are mobile. The adsorption is described using a kinetic equation of Langmuir's type. The simple case of small adsorption is considered, in which the saturation effect can be neglected, and the fundamental equations of the model can be linearized. In this framework, the effective relaxation time describing the dynamics of the system is evaluated, as well as the profiles of the ions and the electric field. The case in which the sample is a half-space is first considered. A more realistic situation where the sample is a slab of thickness $d$, limited by two identical or different electrodes, is analyzed too. The difference in electric potential due to the adsorption phenomenon between the electrodes is determined. Our analysis shows that its time dependence, when the electrodes have different adsorption properties, is not monotonic.
Jason Cantarella et al 2024 J. Phys. A: Math. Theor.
We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of Cantarella, Duplantier, Shonkwiler, and Uehara and has (expected) time per sample quadratic in the number of edges in the polygon. We use our new sampling method and a new code for computing invariants based on the Alexander polynomial to investigate the probability of finding unknots among equilateral closed polygons.
Federico Girotti et al 2024 J. Phys. A: Math. Theor. 57 245304
We revisit the problem of estimating an unknown parameter of a pure quantum state, and investigate 'null-measurement' strategies in which the experimenter aims to measure in a basis that contains a vector close to the true system state. Such strategies are known to approach the quantum Fisher information for models where the quantum Cramér-Rao bound (QCRB) is achievable but a detailed adaptive strategy for achieving the bound in the multi-copy setting has been lacking. We first show that the following naive null-measurement implementation fails to attain even the standard estimation scaling: estimate the parameter on a small sub-sample, and apply the null-measurement corresponding to the estimated value on the rest of the systems. This is due to non-identifiability issues specific to null-measurements, which arise when the true and reference parameters are close to each other. To avoid this, we propose the alternative displaced-null measurement strategy in which the reference parameter is altered by a small amount which is sufficient to ensure parameter identifiability. We use this strategy to devise asymptotically optimal measurements for models where the QCRB is achievable. More generally, we extend the method to arbitrary multi-parameter models and prove the asymptotic achievability of the the Holevo bound. An important tool in our analysis is the theory of quantum local asymptotic normality which provides a clear intuition about the design of the proposed estimators, and shows that they have asymptotically normal distributions.
Markus Frembs and Eric G Cavalcanti 2024 J. Phys. A: Math. Theor.
The Choi-Jamiolkowski isomorphism is an essential component in every quantum information theorist's toolkit: it allows to identify linear maps between two quantum systems with linear operators on the composite system. Here, we analyse this widely used gadget from a new perspective. Namely, we explicitly distinguish between its kinematical and dynamical properties, that is, we study the isomorphism on two different levels: Jordan algebras and the different C∗-algebras they arise from, which are distinguished by their order of composition.
A number of important and novel insights stem from our analysis. We find that Choi's theorem, which asserts that Choi's version of the isomorphism [M.-D. Choi, Lin. Alg. Appl., 10, 285 (1975)] further maps the positive cone of completely positive linear maps (such as quantum channels) to the cone of positive linear operators (such as quantum states) on the composite system, crucially
depends on the dynamical (compositional) structure in C∗-algebras. This in turn lies at the heart of the mismatch between the basis-dependence of Choi's version of the isomorphism, and the basis-independent version by Jamiolkowski [A. Jamiolkowski, Rep. Math. Phys., 3, 275 (1972)]. Here, we overcome this subtle but pervasive issue in a number of ways: first, we prove a version
of Choi's theorem for Jamiolkowski's isomorphism, second, we define a basis-independent variant of Choi's isomorphism and, third, by making explicit the dynamical distinction between Jordan and C∗-algebras, we combine the different variants of the isomorphism into a unified description, that subsumes their individual features. We also embed and interpret our results in the graphical calculus of categorical quantum mechanics.
Kristian Stølevik Olsen and Deepak Gupta 2024 J. Phys. A: Math. Theor. 57 245001
Partial resetting, whereby a state variable x(t) is reset at random times to a value , , generalizes conventional resetting by introducing the resetting strength a as a parameter. Partial resetting generates a broad family of non-equilibrium steady states (NESS) that interpolates between the conventional NESS at strong resetting (a = 0) and a Gaussian distribution at weak resetting (a → 1). Here such resetting processes are studied from a thermodynamic perspective, and the mean cost associated with maintaining such NESS are derived. The resetting phase of the dynamics is implemented by a resetting potential that mediates the resets in finite time. By working in an ensemble of trajectories with a fixed number of resets, we study both the steady-state properties of the propagator and its moments. The thermodynamic work needed to sustain the resulting NESS is then investigated. We find that different resetting traps can give rise to rates of work with widely different dependencies on the resetting strength a. Surprisingly, in the case of resets mediated by a harmonic trap with otherwise free diffusive motion, the asymptotic rate of work is insensitive to the value of a. For general anharmonic traps, the asymptotic rate of work can be either increasing or decreasing as a function of the strength a, depending on the degree of anharmonicity. Counter to intuition, the rate of work can therefore in some cases increase as the resetting becomes weaker although the work vanishes at a = 1. Work in the presence of a background potential is also considered. Numerical simulations confirm our findings.
Nikolaos Papadatos and Dimitris Moustos 2024 J. Phys. A: Math. Theor. 57 245301
We consider a two-level atom that follows a wordline of constant velocity, while interacting with a massless scalar field in a thermal state through: (i) an Unruh–DeWitt (UDW) coupling, and (ii) a coupling that involves the time derivative of the field. We treat the atom as an open quantum system, with the field playing the role of the environment, and employ a master equation to describe its time evolution. We study the dynamics of entanglement between the moving atom and a (auxiliary) qubit at rest and isolated from the thermal field. We find that in the case of the standard UDW coupling and for high temperatures of the environment the decay of entanglement is delayed due to the atom's motion. Instead, in the derivative coupling case, the atom's motion always causes the rapid death of entanglement.
Dmitry Kolyaskin and Vladimir V Mangazeev 2024 J. Phys. A: Math. Theor. 57 245201
We study solutions of the reflection equation related to the quantum affine algebra . First, we explain how to construct a family of stochastic integrable vertex models with fixed boundary conditions. Then, we construct upper- and lower-triangular solutions of the reflection equation related to symmetric tensor representations of with arbitrary spin. We also prove the star–star relation for the Boltzmann weights of the Ising-type model, conjectured by Bazhanov and Sergeev, and use it to verify certain properties of the solutions obtained.