样式: 排序: IF: - GO 导出 标记为已读
-
Stochastic path power and the Laplace transform J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-17 S P Fitzgerald, T J W Honour
Transition probabilities for stochastic systems can be expressed in terms of a functional integral over paths taken by the system. Approximately evaluating this integral by the saddle point method in the weak-noise limit leads to a remarkable mapping between dominant stochastic paths through the potential V and conservative, Hamiltonian mechanics with an effective potential −|∇V|2 . The conserved ‘energy’
-
Noether invariance theory for the equilibrium force structure of soft matter J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-16 Sophie Hermann, Florian Sammüller, Matthias Schmidt
We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether
-
The u(2|2)1 WZW model J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-15 Matthias R Gaberdiel, Elia Mazzucchelli
WZW models based on super Lie algebras play an important role for the description of string theory on AdS spaces. In particular, for the case of AdS3×S3 with pure NS–NS flux the super Lie algebra of psu(1,1|2)k appears in the hybrid formalism, and higher dimensional AdS spaces can be described in terms of related supergroup cosets. In this paper we study the WZW models based on u(2|2)1 and psu(2|2)1
-
Random-matrix model for thermalization J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-09 Hans A Weidenmüller
We show that for a system governed by a random-matrix Hamiltonian (a member of the time-reversal invariant Gaussian Orthogonal Ensemble (GOE) of random matrices of dimension N), all functions Tr(Aρ(t)) in the ensemble thermalize: For N→∞ every such function tends to the value Tr(Aρeq(∞))+Tr(Aρ(0))g2(t) . Here ρ(t) is the time-dependent density matrix of the system, A is a Hermitean operator standing
-
Thermalization of closed chaotic many-body quantum systems J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-09 Hans A Weidenmüller
We investigate thermalization of a closed chaotic many-body quantum system by combining the Hartree–Fock approach with the Bohigas–Giannoni–Schmit conjecture. The conjecture implies that locally, the residual interaction causes the statistics of eigenvalues and eigenfunctions of the full Hamiltonian to agree with random-matrix predictions. The agreement is confined to an interval Δ (the correlation
-
Replica symmetry breaking in supervised and unsupervised Hebbian networks J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-09 Linda Albanese, Andrea Alessandrelli, Alessia Annibale, Adriano Barra
Hebbian neural networks with multi-node interactions, often called Dense Associative Memories, have recently attracted considerable interest in the statistical mechanics community, as they have been shown to outperform their pairwise counterparts in a number of features, including resilience against adversarial attacks, pattern retrieval with extremely weak signals and supra-linear storage capacities
-
Semi-definite programming and quantum information J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-08 Piotr Mironowicz
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
-
Exact exponent for atypicality of random quantum states J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-08 Eyuri Wakakuwa
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of ‘concentration of measure’ and have focused on the behavior of the states close to the average. In contrast, we investigate the large deviation regime, where the
-
Fluctuation theorem as a special case of Girsanov theorem J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-08 Annwesha Dutta, Saikat Sarkar
Stochastic thermodynamics is an important development in the direction of finding general thermodynamic principles for non-equilibrium systems. We believe stochastic thermodynamics has the potential to benefit from the measure-theoretic framework of stochastic differential equations (SDEs). Toward this, in this work, we show that fluctuation theorem (FT) is a special case of the Girsanov theorem, which
-
Improving performance of quantum heat engines using modified Otto cycle J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-05 Revathy B S, Harsh Sharma, Uma Divakaran
The efficiency of a quantum heat engine is maximum when the unitary strokes of the quantum Otto cycle are adiabatic. On the other hand, this may not be always possible due to small energy gaps in the system, especially at the critical point (CP) where the gap between the ground state and the first excited state vanishes and the system gets excited. With the aim to regain this lost adiabaticity, we
-
An invariant measure of chiral quantum transport J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-05 K Ziegler
We study the invariant measure of the transport correlator for a chiral Hamiltonian and analyze its properties. The Jacobian of the invariant measure is a function of random phases. Then we distinguish the invariant measure before and after the phase integration. In the former case we found quantum diffusion of fermions and a uniform zero mode that is associated with particle conservation. After the
-
A review on coisotropic reduction in symplectic, cosymplectic, contact and co-contact Hamiltonian systems J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-05 Manuel de León, Rubén Izquierdo-López
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.
-
Three point amplitudes in matrix theory J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-04 Aidan Herderschee, Juan Maldacena
We compute the three graviton amplitude in the Banks-Fischler-Shenker-Susskind matrix model for M-theory. Even though the three point amplitude is determined by super Poincare invariance in eleven dimensional M-theory, it requires a non-trivial computation in the matrix model. We consider a configuration where all three gravitons carry non-zero longitudinal momentum. To simplify the problem, we compactify
-
Linear statistics for Coulomb gases: higher order cumulants J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-03 Benjamin De Bruyne, Pierre Le Doussal, Satya N Majumdar, Grégory Schehr
We consider N classical particles interacting via the Coulomb potential in spatial dimension d and in the presence of an external trap, at equilibrium at inverse temperature β. In the large N limit, the particles are confined within a droplet of finite size. We study smooth linear statistics, i.e. the fluctuations of sums of the form LN=∑i=1Nf(xi) , where x i ’s are the positions of the particles and
-
Nonequilibrium statistical mechanics of money/energy exchange models J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-02 Maggie Miao, Dmitrii E Makarov, Kristian Blom
Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in
-
Thermodynamic uncertainty relations in the presence of non-linear friction and memory J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-02 A Plati, A Puglisi, A Sarracino
A new thermodynamic uncertainty relation (TUR) is derived for systems described by linearly coupled Langevin equations in the presence of non-linear frictional forces. In our scheme, the main variable represents the velocity of a particle, while the other coupled variables describe memory effects which may arise from strongly correlated degrees of freedom with several time-scales and, in general, are
-
The Jones polynomial in systems with periodic boundary conditions J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-04-02 Kasturi Barkataki, Eleni Panagiotou
Entanglement of collections of filaments arises in many contexts, such as in polymer melts, textiles and crystals. Such systems are modeled using periodic boundary conditions (PBCs), which create an infinite periodic system whose global entanglement may be impossible to capture and is repetitive. We introduce two new methods to assess topological entanglement in PBC: the Periodic Jones polynomial and
-
Minimum and maximum quantum uncertainty states for qubit systems J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-28 Huihui Li, Shunlong Luo, Yue Zhang
We introduce the notion of (renormalized) quantum uncertainty and reveal its basic features. In terms of this quantity, we completely characterize the minimum and maximum quantum uncertainty states for qubit systems involving Pauli matrices. It turns out that the minimum quantum uncertainty states consist of both certain pure states and certain mixed states, in sharp contrast to the case of conventional
-
The nonlinear Schrödinger equation in cylindrical geometries J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-28 R Krechetnikov
The nonlinear Schrödinger equation was originally derived in nonlinear optics as a model for beam propagation, which naturally requires its application in cylindrical coordinates. However, that derivation was performed in Cartesian coordinates for linearly polarized fields with the Laplacian Δ⊥=∂x2+∂y2 transverse to the beam z-direction, and then, tacitly assuming covariance, extended to axisymmetric
-
On different approaches to integrable lattice models J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-28 Vladimir Belavin, Doron Gepner, J Ramos Cabezas, Boris Runov
Interaction-round the face (IRF) models are two-dimensional lattice models of statistical mechanics defined by an affine Lie algebra and admissibility conditions depending on a choice of representation of that affine Lie algebra. Integrable IRF models, i.e. the models the Boltzmann weights of which satisfy the quantum Yang–Baxter equation, are of particular interest. In this paper, we investigate trigonometric
-
Effective rationality for local unitary invariants of mixed states of two qubits J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-27 Luca Candelori, Vladimir Y Chernyak, John R Klein, Nick Rekuski
We calculate the field of rational local unitary invariants for mixed states of two qubits, by employing methods from algebraic geometry. We prove that this field is rational (i.e. purely transcendental), and that it is generated by nine algebraically independent polynomial invariants. We do so by constructing a relative section, in the sense of invariant theory, whose Weyl group is a finite abelian
-
More on symmetry resolved operator entanglement J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-27 Sara Murciano, Jérôme Dubail, Pasquale Calabrese
The ‘operator entanglement’ of a quantum operator O is a useful indicator of its complexity, and, in one-dimension, of its approximability by matrix product operators. Here we focus on spin chains with a global U(1) conservation law, and on operators O with a well-defined U(1) charge, for which it is possible to resolve the operator entanglement of O according to the U(1) symmetry. We employ the notion
-
Topological extension including quantum jump J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-26 Xiangyu Niu, Junjie Wang
Non-Hermitian (NH) systems and the Lindblad form master equation have always been regarded as reliable tools in dissipative modeling. Intriguingly, existing literature often obtains an equivalent NH Hamiltonian by neglecting the quantum jumping terms in the master equation. However, there lacks investigation into the effects of discarded terms as well as the unified connection between these two approaches
-
Open 2–TASEP with integrable boundaries J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-26 Luigi Cantini
In this paper, we explore a two-species extension of the totally asymmetric simple exclusion process (TASEP) known as ‘2–TASEP’ with open boundaries. In this model, carriers on a one-dimensional lattice exhibit distinct behaviors: loaded carriers move right, empty carriers move left, and they exchange positions at a unit rate. At the boundaries carriers are loaded at the left and unloaded at the right
-
Transition path theory for diffusive search with stochastic resetting J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-26 Paul C Bressloff
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states within this energy landscape, and calculating the effective reaction rate. It is now the standard method for analyzing rare events between long lived states. In this
-
Phase space propagation of waves in nonhomogeneous media: corrections beyond the optical geometry limit J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-26 O Morandi
We investigate the corrections to the optical geometry approximation for waves traveling in non homogeneous media. We model the wave propagation in dispersive and non dispersive materials in terms of the phase space Wigner–Weyl formalism. The ray tracing optical geometry limit is introduced by numerical tests. We solve the exact Wigner propagation equation for 1D non dispersive materials. We discuss
-
Rydberg atoms in D dimensions: entanglement, entropy and complexity J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-26 J S Dehesa
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
-
Soliton dynamics and stability in the ABS spinor model with a PT -symmetric periodic complex potential J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-25 Franz G Mertens, Bernardo Sánchez-Rey, Niurka R Quintero
We investigate the effects on solitons dynamics of introducing a PT -symmetric complex potential in a specific family of the cubic Dirac equation in (1+1)-dimensions, called the Alexeeva–Barashenkov–Saxena model. The potential is introduced taking advantage of the fact that the nonlinear Dirac equation admits a Lagrangian formalism. As a consequence, the imaginary part of the potential, associated
-
Maximally entangled real states and SLOCC invariants: the 3-qutrit case J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-22 Hamza Jaffali, Frédéric Holweck, Luke Oeding
The absolute values of polynomial SLOCC invariants (which always vanish on separable states) can be seen as entanglement measures. We study the case of real 3-qutrit systems and discover a new set of maximally entangled states (from the point of view of maximizing the hyperdeterminant). We also study the basic fundamental invariants and find real 3-qutrit states that maximize their absolute values
-
Effects of high-low frequency electromagnetic radiation on vibrational resonance in Hodgkin–Huxley neuronal system J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-22 Kaijun Wu, Jiawei Li
In this paper, based on the Hodgkin–Huxley (H–H) neuron model, the effects of high-low frequency (HLF) electromagnetic radiation on vibrational resonance (VR) in a single neuron is investigated. It is found that VR can be observed in a single H–H neuron model with or without considering HLF electromagnetic radiation. However, HLF electromagnetic radiation can cause changes in the structure of the resonance
-
A delay analogue of the box and ball system arising from the ultra-discretization of the delay discrete Lotka–Volterra equation J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-22 Kenta Nakata, Kanta Negishi, Hiroshi Matsuoka, Ken-ichi Maruno
A delay analogue of the box and ball system (BBS) is presented. This new soliton cellular automaton is constructed by the ultra-discretization of the delay discrete Lotka–Volterra equation, which is an integrable delay analogue of the discrete Lotka–Volterra equation. Soliton patterns generated by this delay BBS are classified into normal solitons and abnormal solitons. Normal solitons have a clear
-
The BMS group in D = 6 spacetime dimensions J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-21 Oscar Fuentealba, Marc Henneaux
The asymptotic structure of gravity in D = 6 spacetime dimensions is described at spatial infinity in the asymptotically flat context through Hamiltonian (ADM) methods. Special focus is given on the Bondi–Metzner–Sachs (BMS) supertranslation subgroup. It is known from previous studies that the BMS group contains more supertranslations as one goes from D = 4 to D = 5. Indeed, while the supertranslations
-
Reply to Comment on ‘Anomalous diffusion originated by two Markovian hopping-trap mechanisms’ J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-20 S Vitali, P Paradisi, G Pagnini
Reply to V P Shkilev.
-
Riemannian quantum circuit optimization for Hamiltonian simulation J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-20 Ayse Kotil, Rahul Banerjee, Qunsheng Huang, Christian B Mendl
Hamiltonian simulation, i.e. simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful approximation can lead to relatively deep circuits. Here we start from the insight that for translation invariant systems, the gates in such circuit topologies can
-
Comment on ‘Anomalous diffusion originated by two Markovian hopping-trap mechanisms’ J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-20 V P Shkilev
The authors of the paper (Vitali et al 2022 J. Phys. A: Math. Theor. 55 224012) analyzed a simple CTRW model with a waiting time distribution defined as the weighted sum of two exponential distributions. They showed that their model meets many paradigmatic features that belong to the anomalous diffusion as it is observed in living systems. This comment point out the previous paper that considers a
-
Adiabatic theorem for classical stochastic processes J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-20 Kazutaka Takahashi
We apply adiabatic theorems developed for quantum mechanics to stochastic annealing processes described by the classical master equation with a time-dependent generator. When the instantaneous stationary state is unique and the minimum decay rate g is nonzero, the time-evolved state is basically relaxed to the instantaneous stationary state. By formulating an asymptotic expansion rigorously, we derive
-
Phase compensation of a continuous-variable quantum key distribution via temporal convolutional neural network J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-20 Wenqi Jiang, Zhiyue Zuo, Gaofeng Luo, Hang Zhang, Ying Guo
Although the continuous-variable quantum key distribution (CV-QKD) protocol based on a local local oscillator (LLO) can close all the security loopholes from the transmitted local oscillator (TLO), the phase noise caused by the inaccurate phase reference information limits the performance of the protocol. To reduce the residual phase noise, in this work, we propose a phase estimation and compensation
-
Search algorithm on strongly regular graph by lackadaisical quantum walk J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-19 Fangjie Peng, Meng Li, Xiaoming Sun
Quantum walk is a widely used method in designing quantum algorithms. In this article, we consider the lackadaisical discrete-time quantum walk (DTQW) on strongly regular graphs (SRG). When there is a single marked vertex in a SRG, we prove that lackadaisical DTQW can find the marked vertex with asymptotic success probability 1, with a quadratic speedup compared to classical random walk. This paper
-
Force-induced desorption of copolymeric comb polymers J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-19 E J Janse van Rensburg, C E Soteros, S G Whittington
We investigate a lattice model of comb copolymers that can adsorb at a surface and that are subject to a force causing desorption. The teeth (the comb’s side chains) and the backbone of the comb are chemically distinct and can interact differently with the surface. That is, the strength of the surface interaction can be different for the monomers in the teeth and in the backbone. We consider several
-
(Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-18 Vasileios A Letsios
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 ( N⩾3 ) de Sitter (dS) spacetime (dS N ) are non-unitary unless N = 4. The (non-)unitarity was demonstrated by simply observing that there is a (mis-)match between the representation-theoretic
-
A proposal to characterize and quantify superoscillations J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-18 Yu Li, José Polo-Gómez, Eduardo Martín-Martínez
We present a formal definition of superoscillating function. We discuss the limitations of previously proposed definitions and illustrate that they do not cover the full gamut of superoscillatory behaviors. We demonstrate the suitability of the new proposal with several examples of well-known superoscillating functions that were not encompassed by previous definitions.
-
Superintegrability and deformed oscillator realizations of quantum TTW Hamiltonians on constant-curvature manifolds and with reflections in a plane J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-15 Ian Marquette, Anthony Parr
We extend the method for constructing symmetry operators of higher order for two-dimensional quantum Hamiltonians by Kalnins et al (2010 J. Phys. A: Math. Theor. 43 265205). This expansion method expresses the integral in a finite power series in terms of lower degree integrals so as to exhibit it as a first-order differential operators. One advantage of this approach is that it does not require the
-
Inertia of partial transpose of positive semidefinite matrices J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-14 Yixuan Liang, Jiahao Yan, Dongran Si, Lin Chen
We show that the partial transpose of 9×9 positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4) . It solves an open problem in ‘LINEAR AND MULTILINEAR ALGEBRA. Changchun Feng et al, 2022’. We apply our results to construct some inertia, as well as present the list of all possible inertia of partial transpose of 12×12 positive semidefinite matrices.
-
The establishment of uncertain single pendulum equation and its solutions * J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-12 Xiaoyue Qiu, Jiaxuan Zhu, Shiqin Liu, Liying Liu
The single pendulum equation is commonly used to model the vibration characteristics of a single pendulum subjected to variable forces. A stochastic single pendulum equation driven by Wiener process describes the vibration phenomenon containing a noise term. However, there are also contradictions in some cases. Therefore, in this paper, uncertain single pendulum equation driven by Liu process is proposed
-
Exact solutions of steady Euler equations in two dimension by functional separation J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-12 Sun-Chul Kim
Exact solutions of two dimensional Euler equations for incompressible fluid flows are found by the functional separation of variables. More specifically, two independent variables are considered in the Cartesian coordinates, polar coordinates and also general orthogonal curvilinear coordinates which include elliptic, parabolic and hyperbolic systems. Several new solutions are obtained and other classical
-
Canonical reductions of the TED equation: integrable deformations of heavenly-type equations J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-12 B G Konopelchenko, W K Schief
Natural classes of integrability-preserving reductions of a 4+4-dimensional generalisation (TED equation) of the general heavenly equation are recorded. In particular, these reductions lead to integrable ‘deformations’ of various other avatars of the heavenly equation governing self-dual Einstein spaces. The known deformed heavenly equations which give rise to half-flat conformal structures are retrieved
-
Ising model on the aperiodic Smith hat J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-12 Yutaka Okabe, Komajiro Niizeki, Yoshiaki Araki
Smith et al discovered an aperiodic monotile of 13 sided shape in 2023. It is called the ‘Smith hat’ and consists of eight kites. We deal with the statistical physics of the lattice of the kites, which we call the ‘Smith-kite lattice’. We studied the Ising model on the aperiodic Smith-kite lattice and the dual Smith-kite lattice using Monte Carlo simulations. We combined the Swendsen–Wang multi-cluster
-
Corrigendum: Quantum state estimation with nuisance parameters (2020 J. Phys. A: Math. Theor. 53 453001) J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-11 Jun Suzuki, Yuxiang Yang, Masahito Hayashi
This is a correction for Suzuki et al (2020 J. Phys. A: Math. Gen. 53 453001).
-
Replica analysis of overfitting in regression models for time to event data: the impact of censoring J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-11 E Massa, A Mozeika, A C C Coolen
We use statistical mechanics techniques, viz. the replica method, to model the effect of censoring on overfitting in Cox’s proportional hazards model, the dominant regression method for time-to-event data. In the overfitting regime, Maximum Likelihood (ML) parameter estimators are known to be biased already for small values of the ratio of the number of covariates over the number of samples. The inclusion
-
Gibbs sampling the posterior of neural networks J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-11 Giovanni Piccioli, Emanuele Troiani, Lenka Zdeborová
In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an efficient Gibbs sampler. For small models, the Gibbs sampler attains similar performances as the state-of-the-art Markov chain Monte Carlo methods
-
Solvable non-Hermitian skin effects and real-space exceptional points: non-Hermitian generalized Bloch theorem J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-08 Xintong Zhang, Xiaoxiao Song, Shubo Zhang, Tengfei Zhang, Yuanjie Liao, Xinyi Cai, Jing Li
Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates
-
Tunneling in soft waveguides: closing a book J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-08 Pavel Exner, David Spitzkopf
We investigate the spectrum of a soft quantum waveguide in two dimensions of the generalized ‘bookcover’ shape, that is, Schrödinger operator with the potential in the form of a ditch consisting of a finite curved part and straight asymptotes which are parallel or almost parallel pointing in the same direction. We show how the eigenvalues accumulate when the angle between the asymptotes tends to zero
-
Spectral properties of the Bloch–Torrey operator in three dimensions J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-08 Denis S Grebenkov
We consider the Bloch–Torrey operator, −Δ+igx , that governs the time evolution of the transverse magnetization in diffusion magnetic resonance imaging (dMRI). Using the matrix formalism, we compute numerically the eigenvalues and eigenfunctions of this non-Hermitian operator for two bounded three-dimensional domains: a sphere and a capped cylinder. We study the dependence of its eigenvalues and eigenfunctions
-
Operator algebra generalization of a theorem of Watrous and mixed unitary quantum channels J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-07 David W Kribs, Jeremy Levick, Rajesh Pereira, Mizanur Rahaman
We establish an operator algebra generalization of Watrous’ theorem (Watrous 2009 Quantum Inf. Comput. 9 403–413) on mixing unital quantum channels (completely positive trace-preserving maps) with the completely depolarizing channel, wherein the more general objects of focus become (finite-dimensional) von Neumann algebras, the unique trace preserving conditional expectation onto the algebra, the group
-
Anomalous non-Gaussian diffusion of scaled Brownian motion in a quenched disorder environment J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-07 Kheder Suleiman, Yongge Li, Yong Xu
This paper aims to investigate particle dynamics in a random environment, subjected to power-law time-dependent temperature. To this end, the scaled Brownian motion (SBM), a stochastic process described by a diffusion equation with time-dependent diffusivity, has been studied numerically in quenched disordered systems (QDLs). Here, QDLs have been modeled by spatial correlated Gaussian random potential
-
On a problem due to Glasser on analytically tractable moments J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-06 John M Campbell
Glasser, in 2011, introduced a remarkable integral identity of physical interest and suggested that the evaluation ∫01/2kK2(k)dk=πG4 provides the unique analytically tractable moment of K 2 on a sub-unit interval, where K denotes the complete elliptic integral of the first kind, and where G=112−132+152−⋯ denotes Catalan’s constant. We show how a case of Clausen’s product identity related to Ramanujan’s
-
Positive maps from the walled Brauer algebra J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-06 Maria Balanzó-Juandó, Michał Studziński, Felix Huber
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one correspondence with elements from the walled Brauer algebra. Using our formalism, these maps can be obtained in a systematic and clear way by manipulating partially transposed
-
Uncovering exceptional contours in non-Hermitian hyperbolic lattices J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-06 Nisarg Chadha, Awadhesh Narayan
Hyperbolic lattices are starting to be explored in search of novel phases of matter. At the same time, non-Hermitian physics has come to the forefront in photonic, optical, phononic, and condensed matter systems. In this work, we introduce non-Hermitian hyperbolic lattices and elucidate its exceptional properties in depth. We use hyperbolic Bloch theory to investigate band structures of hyperbolic
-
The importance of the local structure of fractal aggregates J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-06 Robert Botet, Pascal Rannou, Ryo Tazaki
The pair correlation function, g(r), is a fundamental descriptor of the inner structure of fractal aggregates of monomers. It provides a natural tool for studying physical properties involving two-point interaction (e.g. optics of aggregates). Several domains of distances between pairs of monomers have been identified. The fractal domain (in which g(r) is a power-law) is generally dominant for large
-
Wigner transport in linear electromagnetic fields J. Phys. A: Math. Theor. (IF 2.1) Pub Date : 2024-03-05 C Etl, M Ballicchia, M Nedjalkov, J Weinbub
Applying a Weyl–Stratonovich transform to the evolution equation of the Wigner function in an electromagnetic field yields a multidimensional gauge-invariant equation which is numerically very challenging to solve. In this work, we apply simplifying assumptions for linear electromagnetic fields and the evolution of an electron in a plane (two-dimensional transport), which reduces the complexity and