Mathematical Physics

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New submissions for Thu, 9 May 24

[1]  arXiv:2405.04672 [pdf, other]

Title: Enhanced Lieb-Robinson bounds for a class of Bose-Hubbard type Hamiltonians

Authors: Tomotaka Kuwahara, Marius Lemm

Comments: 41 pages, 2 figures

Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

Several recent works have considered Lieb-Robinson bounds (LRBs) for Bose-Hubbard-type Hamiltonians. For certain special classes of initial states (e.g., states with particle-free regions or perturbations of stationary states), the velocity of information propagation was bounded by a constant in time, $v\leq C$, similarly to quantum spin systems. However, for the more general class of bounded-density initial states, the first-named author together with Vu and Saito derived the velocity bound $v\leq C t^{D-1}$, where $D$ is the spatial lattice dimension. For $D\geq 2$, this bound allows for accelerated information propagation. It has been known since the work of Eisert and Gross that some systems of lattice bosons are capable of accelerated information propagation. It is therefore a central question to understand under what conditions the bound $v\leq C t^{D-1}$ can be enhanced. Here, we prove that additional physical constraints, translation-invariance and a $p$-body repulsion of the form $n_x^p$ with $p>D+1$, lead to a LRB with $v\leq C t^{\frac{D}{p-D-1}}$ for any initial state of bounded energy density. We also identify examples of quantum states which show that no further enhancement is possible without using additional dynamical constraints.

[2]  arXiv:2405.04683 [pdf, ps, other]

Title: Multicomplex Ideals, Modules and Hilbert Spaces

Authors: Derek Courchesne, Sébastien Tremblay

Comments: 28 pages

Subjects: Mathematical Physics (math-ph); Rings and Algebras (math.RA)

In this article we study some algebraic aspects of multicomplex numbers $\mathbb M_n$. A canonical idempotent representation defined in terms of $n$ multicomplex conjugates is introduced. This representation facilitates computations in this algebra and makes it possible to introduce a generalized conjugacy, i.e. a composition of the $n$ multicomplex conjugates, as well as a multicomplex norm. The ideals of the ring of multicomplex numbers are then studied. Multicomplex free modules and their linear operators are introduced. Finally, we develop multicomplex Hilbert spaces.

[3]  arXiv:2405.04712 [pdf, other]

Title: Tube Formulae for Generalized von Koch Fractals through Scaling Functional Equations

Authors: Will Hoffer

Comments: 49 pages, 8 figures, for submission to J. Fractal Geom

Subjects: Mathematical Physics (math-ph)

In this work, we provide a treatment of scaling functional equations in a general setting involving fractals arising from sufficiently nice self-similar systems in order to analyze the tube functions, tube zeta functions, and complex dimensions of relative fractal drums. Namely, we express the volume of a tubular neighborhood in terms of scaled copies of itself and a remainder term and then solve this expression by means of the tube zeta functions.
We then apply our methods to analyze these generalized von Koch fractals, which are a class of fractals that allow for different regular polygons and scaling ratios to be used in the construction of the standard von Koch curve and snowflake. In particular, we describe the volume of an inner tubular neighborhoods and the possible complex dimensions of such fractal snowflakes.

[4]  arXiv:2405.05056 [pdf, other]

Title: Large N limit of fuzzy geometries coupled to fermions

Authors: Masoud Khalkhali, Nathan Pagliaroli, Luuk S. Verhoeven

Comments: 37 pages, 10 figures

Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Operator Algebras (math.OA); Quantum Algebra (math.QA)

In this paper we present an analysis of the large N limit of a family of quartic Dirac ensembles based on (0, 1) fuzzy geometries that are coupled to fermions. These Dirac ensembles are examples of single-matrix, multi-trace matrix ensembles. Additionally, they serve as examples of integer-valued $\beta$-ensembles. Convergence of the spectral density in the large N limit for a large class of such matrix ensembles is proven, improving on existing results. The main results of this paper are the addition of the fermionic contribution in the matrix ensemble and the investigation of spectral estimators for finite dimensional spectral triples

[5]  arXiv:2405.05159 [pdf, ps, other]

Title: Finding all solutions to the KZ equations in characteristic $p$

Authors: Alexander Varchenko, Vadim Vologodsky

Comments: LaTex, 40 pages

Subjects: Mathematical Physics (math-ph); Algebraic Geometry (math.AG); Number Theory (math.NT)

The KZ equations are differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level. They form a system of complex partial differential equations with regular singular points satisfied by the $n$-point functions of affine primary fields. In [SV1] the KZ equations were identified with equations for flat sections of suitable Gauss-Manin connections, and solutions of the KZ equations were constructed in the form of multidimensional hypergeometric integrals. In [SV2] the KZ equations were considered modulo a prime number $p$, and polynomial solutions of the KZ equations modulo $p$ were constructed by an elementary procedure as suitable $p$-approximations of the hypergeometric integrals. In this paper we address the problem of whether all solutions of the KZ equations modulo $p$ are generated by the $p$-hypergeometric solutions. We consider the first nontrivial example of the KZ equations and demonstrate that, indeed, in this case, all solutions of the KZ equations modulo $p$ stem from the $p$-hypergeometric solutions.

[6]  arXiv:2405.05228 [pdf, ps, other]

Title: Generalized vector potential and Trace Theorem for Lipschitz domains

Authors: Zhen Liu, Jinbiao Wu

Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Functional Analysis (math.FA)

The vector potential is a fundamental concept widely applied across various fields. This paper presents an existence theorem of a vector potential for divergence-free functions in $W^{m,p}(\mathbb{R}^N,\mathbb{T})$ with general $m,p,N$. Based on this theorem, one can establish the space decomposition theorem for functions in $W^{m,p}_0(\operatorname{curl};\Omega,\mathbb{R}^N)$ and the trace theorem for functions in $W^{m,p}(\Omega)$ within the Lipschitz domain $\Omega \subset \mathbb{R}^N$. The methods of proof employed in this paper are straightforward, natural, and consistent.

[7]  arXiv:2405.05233 [pdf, ps, other]

Title: Classical Grand Angular Momentum in N-Body Problems

Authors: Zhongqi Liang, Jesús Pérez-Ríos

Comments: 8 pages, 3 figures

Subjects: Mathematical Physics (math-ph)

The concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree representation for Jacobi and hyperspherical coordinates, we found a decomposition of its magnitude into magnitudes of one-body angular momenta in 3 dimensions. We generalized some results from the two-body problem. Furthermore, we derive the general expression for the scattering angle for the N-body problem.

[8]  arXiv:2405.05251 [pdf, other]

Title: Radiative corrections to the dynamics of a tracer particle coupled to a Bose scalar field

Authors: Esteban Cárdenas, David Mitrouskas

Comments: 38 pages, 2 figures

Subjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

We consider a tracer particle coupled to a Bose scalar field and study the regime where the field's propagation speed approaches infinity. For initial states devoid of field excitations, we introduce an effective approximation of the time-evolved wave function and prove its validity in Hilbert space norm. In this approximation, the field remains in the vacuum state while the tracer particle propagates with a modified dispersion relation. Physically, the new dispersion relation can be understood as the effect of radiative corrections due to interactions with virtual bosons. Mathematically, it is defined as the solution of a self-consistent equation, whose form depends on the relevant time scale.

Cross-lists for Thu, 9 May 24

[9]  arXiv:2404.15233 (cross-list from hep-th) [pdf, ps, other]

Title: Towards field theory of multiple D0-branes. Hamiltonian mechanics and quantization of simplest 3D prototype of multiple D0-brane system

Authors: Igor Bandos, Unai D.M. Sarraga

Comments: V2: Misprints corrected

Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)

Recently we have constructed a completely supersymmetric nonlinear action possessing the properties expected from multiple D0-brane system. Its quantization should result in an interesting supersymmetric field theory in the (super)space with additional matrix coordinates which can provide an important insights in the study of String Theory. As a first stage toward this aim, in this paper we construct the Hamiltonian mechanics and perform covariant quantization of the simplest three dimensional counterpart of the ten dimensional multiple D0-brane model. We obtain a supersymmetric system of equations in super-spacetime enlarged by bosonic and fermionic matrix coordinates which appears as a result of such quantization and discuss some of its properties.

[10]  arXiv:2405.04599 (cross-list from quant-ph) [pdf, other]

Title: Complex Scaling Method applied to the study of the Swanson Hamiltonian in the broken PT-symmetry phase

Authors: Viviano Fernández, Romina Ramírez, Marta Reboiro

Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

In this work, we study the non-PT symmetry phase of the Swanson Hamiltonian in the framework of the Complex Scaling Method. By constructing a bi-orthogonality relation, we apply the formalism of the response function to analyse the time evolution of different initial wave packages. The Wigner Functions and mean value of operators are evaluated as a function of time. We analyse in detail the time evolution in the neighbourhood of Exceptional Points. We derive a continuity equation for the system. We compare the results obtained using the Complex Scaling Method to the ones obtained by working in a Rigged Hilbert Space.

[11]  arXiv:2405.04619 (cross-list from hep-th) [pdf, other]

Title: Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs

Authors: Pavel Putrov, Rajath Radhakrishnan

Comments: 72 pages, 24 figures

Subjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Quantum Algebra (math.QA)

We study the anomalies of non-invertible symmetries in 1+1D QFTs using gapped boundaries of its SymTFT. We establish the explicit relation between Lagrangian algebras which determine gapped boundaries of the SymTFT, and algebras which determine non-anomalous/gaugeable topological line operators in the 1+1D QFT. If the Lagrangian algebras in the SymTFT are known, this provides a method to compute algebras in all fusion categories that share the same SymTFT. We find necessary conditions that a line operator in the SymTFT must satisfy for the corresponding line operator in the 1+1D QFT to be non-anomalous. We use this constraint to show that a non-invertible symmetry admits a 1+1D trivially gapped phase if and only if the SymTFT admits a magnetic Lagrangian algebra. We define a process of transporting non-anomalous line operators between fusion categories which share the same SymTFT and apply this method to the three Haagerup fusion categories.

[12]  arXiv:2405.04649 (cross-list from math.AT) [pdf, other]

Title: The Smith Fiber Sequence of Invertible Field Theories

Authors: Arun Debray, Sanath K. Devalapurkar, Cameron Krulewski, Yu Leon Liu, Natalia Pacheco-Tallaj, Ryan Thorngren

Comments: 73 pages, 3 figures. Originally posted as the mathematical sections of arXiv:2309.16749. This version features new content in sections 6 and 8

Subjects: Algebraic Topology (math.AT); Mathematical Physics (math-ph)

Smith homomorphisms are maps between bordism groups that change both the dimension and the tangential structure. We give a completely general account of Smith homomorphisms, unifying the many examples in the literature. We provide three definitions of Smith homomorphisms, including as maps of Thom spectra, and show they are equivalent. Using this, we identify the cofiber of the spectrum-level Smith map and extend the Smith homomorphism to a long exact sequence of bordism groups, which is a powerful computation tool. We discuss several examples of this long exact sequence, relating them to known constructions such as Wood's and Wall's sequences. Furthermore, taking Anderson duals yields a long exact sequence of invertible field theories, which has a rich physical interpretation. We developed the theory in this paper with applications in mind to symmetry breaking in quantum field theory, which we study in a companion paper.

[13]  arXiv:2405.04720 (cross-list from math.AP) [pdf, ps, other]

Title: Convergence Rate of the Hypersonic Similarity for Two-Dimensional Steady Potential Flows with Large Data

Authors: Gui-Qiang G. Chen, Jie Kuang, Wei Xiang, Yongqian Zhang

Comments: 47 pages, 11 figures

Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)

We establish the optimal convergence rate of the hypersonic similarity for two-dimensional steady potential flows with {\it large data} past over a straight wedge in the $BV\cap L^1$ framework, provided that the total variation of the large data multiplied by $\gamma-1+\frac{a_{\infty}^2}{M_\infty^2}$ is uniformly bounded with respect to the adiabatic exponent $\gamma>1$, the Mach number $M_\infty$ of the incoming steady flow, and the hypersonic similarity parameter $a_\infty$. Our main approach in this paper is first to establish the Standard Riemann Semigroup of the initial-boundary value problem for the isothermal hypersonic small disturbance equations with large data and then to compare the Riemann solutions between two systems with boundary locally case by case. Based on them, we derive the global $L^1$--estimate between the two solutions by employing the Standard Riemann Semigroup and the local $L^1$--estimates. We further construct an example to show that the convergence rate is optimal.

[14]  arXiv:2405.04772 (cross-list from hep-th) [pdf, other]

Title: Cluster Alphabets from Generalized Worldsheets: A Geometric Approach to Finite Types

Authors: Peng Zhao, Yihong Wang

Journal-ref: Phys. Rev. D 108, 105013 (2023)

Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

We provide a systematic derivation of cluster alphabets of finite types. The construction is based on a geometric realization of the generalized worldsheets by gluing and folding a pair of polygons. The cross ratios of the worldsheet z variables are evolved using the Y-system equations. By a new gauge choice, we obtain a simpler set of cluster alphabets than the known ones.

[15]  arXiv:2405.04827 (cross-list from math.DG) [pdf, ps, other]

Title: The Geometry of Three-Forms on Symplectic Six-Manifolds

Authors: Teng Fei

Comments: 34 pages, all comments are welcome!

Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph); Complex Variables (math.CV); Symplectic Geometry (math.SG)

In this paper, we investigate the geometry associated with 3-forms of various orbital type on a symplectic 6-manifold. We show that there are extremely rich geometric structures attached to certain unstable 3-forms arising naturally from degeneration of Calabi-Yau structures, which in turn provides us a new perspective towards the SYZ conjecture. We give concrete examples and demonstrate that the limiting behavior of the Type IIA flow can be used to detect canonical geometric structures on symplectic manifolds.

[16]  arXiv:2405.04956 (cross-list from cond-mat.stat-mech) [pdf, ps, other]

Title: Modified version of open TASEP with dynamic defects

Authors: Nikhil Bhatia, Arvind Kumar Gupta

Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

We propose a modification to the study of site-wise dynamically disordered totally asymmetric simple exclusion process (TASEP). Motivated by the process of gene transcription, a study in ref. [39] introduced an extension of TASEP, where the defects (or obstacles) bind/un-bind dynamically to the sites of the lattice and the hopping of the particles on lattice faces a hindrance if the arrival site is occupied by an obstacle. In addition, the particle is only allowed to enter the lattice provided the first site is defect-free. In our study, we propose that the particle movement at the entry of the lattice must face an equal hindrance that is provided by the obstacles to the rest of the particles on the lattice. For open boundaries, the continuum mean-field equations are derived and solved numerically to obtain steady-state phase diagrams and density profiles. The presence of obstacles produces a shift in the phase boundaries obtained but the same three phases as obtained for the standard TASEP. Contrary to the model introduced in ref. \cite{waclaw2019totally}, the idea to introduce the modification at the entrance shows that the limiting case $p_d \rightarrow 1$ converges to the standard TASEP, where $p_d$ refers to the affected hopping rate due to presence of obstacle. The mean-field solutions are validated using extensive Monte Carlo simulations.

[17]  arXiv:2405.04981 (cross-list from astro-ph.HE) [pdf, other]

Title: A unified theory of the self-similar supersonic Marshak wave problem

Authors: Menahem Krief, Ryan G. McClarren

Comments: Accepted for publications in Physics of Fluids

Subjects: High Energy Astrophysical Phenomena (astro-ph.HE); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph); Fluid Dynamics (physics.flu-dyn); Plasma Physics (physics.plasm-ph)

We present a systematic study of the similarity solutions for the Marshak wave problem, in the local thermodynamic equilibrium (LTE) diffusion approximation and in the supersonic regime. Self-similar solutions exist for a temporal power law surface temperature drive and a material model with power law temperature dependent opacity and energy density. The properties of the solutions in both linear and nonlinear conduction regimes are studied as a function of the temporal drive, opacity and energy density exponents. We show that there exists a range of the temporal exponent for which the total energy in the system decreases, and the solution has a local maxima. For nonlinear conduction, we specify the conditions on the opacity and energy density exponents under which the heat front is linear or even flat, and does posses its common sharp character; this character is independent of the drive exponent. We specify the values of the temporal exponents for which analytical solutions exist and employ the Hammer-Rosen perturbation theory to obtain highly accurate approximate solutions, which are parameterized using only two numerically fitted quantities. The solutions are used to construct a set of benchmarks for supersonic LTE radiative heat transfer, including some with unusual and interesting properties such as local maxima and non sharp fronts. The solutions are compared in detail to implicit Monte-Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which highlights their usefulness as a verification test problem for radiative transfer simulations.

[18]  arXiv:2405.05002 (cross-list from physics.optics) [pdf, other]

Title: Tunable Localisation in Parity-Time-Symmetric Resonator Arrays with Imaginary Gauge Potentials

Authors: Habib Ammari, Silvio Barandun, Ping Liu, Alexander Uhlmann

Subjects: Optics (physics.optics); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)

The aim of this paper is to illustrate both analytically and numerically the interplay of two fundamentally distinct non-Hermitian mechanisms in a deep subwavelength regime. Considering a parity-time symmetric system of one-dimensional subwavelength resonators equipped with two kinds of non-Hermiticity - an imaginary gauge potential and on-site gain and loss - we prove that all but two eigenmodes of the system decouple when going through an exceptional point. By tuning the gain-to-loss ratio, the system changes from a phase with unbroken parity-time symmetry to a phase with broken parity-time symmetry. At the macroscopic level, this is observed as a transition from symmetrical eigenmodes to condensated eigenmodes at one edge of the structure. Mathematically, it arises from a topological state change. The results of this paper open the door to the justification of a variety of phenomena arising from the interplay between non-Hermitian reciprocal and non-reciprocal mechanisms not only in subwavelength wave physics but also in quantum mechanics where the tight binding model coupled with the nearest neighbour approximation can be analysed with the same tools as those developed here.

[19]  arXiv:2405.05045 (cross-list from math.PR) [pdf, ps, other]

Title: Maximum of the Characteristic Polynomial of I.I.D. Matrices

Authors: Giorgio Cipolloni, Benjamin Landon

Comments: 85 pages

Subjects: Probability (math.PR); Mathematical Physics (math-ph)

We compute the leading order asymptotic of the maximum of the characteristic polynomial for i.i.d. matrices with real or complex entries. In particular, this result is new even for real Ginibre matrices, which was left as an open problem in [arXiv:2303.09912]; the complex Ginibre case was covered in [arXiv:1902.01983]. These are the first universality results for the non--Hermitian analog of the first order term of the Fyodorov--Hiary--Keating conjecture. Our methods are based on constructing a coupling to the branching random walk via Dyson Brownian motion. In particular, we find a new connection between real i.i.d. matrices and inhomogeneous branching random walk.

[20]  arXiv:2405.05163 (cross-list from quant-ph) [pdf, other]

Title: Fast Fourier transforms and fast Wigner and Weyl functions in large quantum systems

Authors: C. Lei, A. Vourdas

Journal-ref: Eur. Phys. J. Plus 139, 394 (2024)

Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph)

Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space $D=d^n$ with $d$ an odd integer, and is inspired by the Cooley-Tukey formalism. The `large Fourier transform' is expressed as a sequence of $n$ `small Fourier transforms' (together with some other transforms) in quantum systems with $d$-dimensional Hilbert space. Limitations of the method are discussed. In some special cases, the $n$ Fourier transforms can be performed in parallel. The second method is for systems with dimension of the Hilbert space $D=d_0...d_{n-1}$ with $d_0,...,d_{n-1}$ odd integers coprime to each other. It is inspired by the Good formalism, which in turn is based on the Chinese reminder theorem. In this case also the `large Fourier transform' is expressed as a sequence of $n$ `small Fourier transforms' (that involve some constants related to the number theory that describes the formalism). The `small Fourier transforms' can be performed in a classical computer or in a quantum computer (in which case we have the additional well known advantages of quantum Fourier transform circuits). In the case that the small Fourier transforms are performed with a classical computer, complexity arguments for both methods show the reduction in computational time from ${\cal O}(D^2)$ to ${\cal O}(D\log D)$. The second method is also used for the fast calculation of Wigner and Weyl functions, in quantum systems with large finite dimension of the Hilbert space.

[21]  arXiv:2405.05178 (cross-list from hep-th) [pdf, other]

Title: Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography

Authors: Yoshiki Fukusumi

Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph)

Generalized symmetry, including non-invertible and categorical symmetry, plays a central role in contemporary studies on topological orders (TOs) and the corresponding conformal field theories (CFTs). The generators of such symmetries have a close connection to non-abelian anyonic objects in a bulk CFT or chiral CFT (CCFT), but it has been known that the construction of a CCFT contains theoretical difficulties in general. In this work, we revisit the structure of the fusion rule in $Z_{N}$ symmetric chiral and bulk conformal field theories and the corresponding TOs. We propose a nontrivial expression of subalgebra structure in the fusion rule of a bulk CFT. We name this subalgebra "bulk semionization" which corresponds to the fusion rule of the CCFTs and categorical symmetry of the TOs. This is a bulk-edge correspondence based on the symmetry analysis and can be interpreted as a version of topological holography in the recent literature. The topological holography has been expected to be applicable to the systems in general space-time dimensions. Moreover, we give a concise way of unifying duality (or fractional supersymmetry), generalized or categorical symmetry, and Lagrangian subalgebra. Our method is potentially useful to formulate and study general TOs, fundamentally only from the data of bulk CFTs.

Replacements for Thu, 9 May 24

[22]  arXiv:2210.15148 (replaced) [pdf, other]

Title: Ranking Edges by their Impact on the Spectral Complexity of Information Diffusion over Networks

Authors: Jeremy Kazimer, Manlio de Domenico, Peter J. Mucha, Dane Taylor

Comments: 27 pages, 9 figures. Revision based on submission to SIAM MMS journal

Subjects: Physics and Society (physics.soc-ph); Information Theory (cs.IT); Mathematical Physics (math-ph)

[23]  arXiv:2305.00662 (replaced) [pdf, other]

Title: Eigenstate thermalization in an open bipartite quantum system and the semiclassical method base on correlations of adjacent local states in phase space

Authors: Chen-Huan Wu

Subjects: Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

[24]  arXiv:2306.16323 (replaced) [pdf, other]

Title: Jacobi Beta Ensemble and $b$-Hurwitz Numbers

Authors: Giulio Ruzza

Journal-ref: SIGMA 19 (2023), 100, 18 pages

Subjects: Mathematical Physics (math-ph); Combinatorics (math.CO)

[25]  arXiv:2307.00788 (replaced) [pdf, ps, other]

Title: Positive mass gap of quantum Yang-Mills Fields

Authors: Adrian P. C. Lim

Comments: 95 pages

Subjects: Mathematical Physics (math-ph)

[26]  arXiv:2312.12517 (replaced) [pdf, other]

Title: Flux Quantization on Phase Space

Authors: Hisham Sati, Urs Schreiber

Comments: 23 pages; v3: published version, with a little more background added to section 3.1; v2: more references added & typos fixed

Journal-ref: Annales Henri Poincar\'e (2024)

Subjects: High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Algebraic Topology (math.AT); Differential Geometry (math.DG); K-Theory and Homology (math.KT)

[27]  arXiv:2312.17565 (replaced) [pdf, other]

Title: Thermodynamics of the five-vertex model with scalar-product boundary conditions

Authors: Ivan N. Burenev, Andrei G. Pronko

Comments: 52 pages, 7 figures; v2: Sections 1, 4, and 5 extended, references added

Subjects: Mathematical Physics (math-ph); Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR)

[28]  arXiv:2404.11501 (replaced) [pdf, other]

Title: Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras

Authors: Pramod Padmanabhan, Vladimir Korepin

Comments: v2 70 pages, Includes missing solutions, all of which are succinctly captured in Theorems 1 and 2

Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

[29]  arXiv:2404.15561 (replaced) [pdf, ps, other]

Title: Casimir energy on the sphere and 6D CFT trace anomaly

Authors: R. Aros, F. Bugini, D.E. Díaz, C. Núñez-Barra

Comments: 14 pages. No figures. Three Tables. Version two. References added and new appendix included

Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)

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• Replacements