数学物理
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension $d \leq 3$, vanishing Chern classes of bundles of Bloch eigenfunctions characterize operators with exponentially…
The celebrated Evans-Searles, respectively Gallavotti-Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper,…
In their recent works [Comm. Math. Phys. 399:1 (2023)] and [arXiv:2109.01094], Michelen and Perkins proved that the pressure of a system of particles with repulsive pair interactions is analytic for activities up to…
In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high…
Recently, Benedikter and the author proved an approximate formula for the momentum distribution of a 3d fermionic gas interacting by a short-range pair potential in the mean-field regime, within a trial state close to the ground state.…
We provide a rigorous construction of a large class of generalized spin-boson models with ultraviolet-divergent form factors. This class comprises various models of many possibly non-identical atoms with arbitrary but finite numbers of…
We construct an extension of Fock space and prove that it allows for implementing bosonic Bogoliubov transformations in a certain extended sense. While an implementation in the regular sense on Fock space is only possible if a certain…
We provide two extensions of a dense subspace of Fock space, such that Bogoliubov transformations become implementable on them, even though they violate the Shale-Stinespring condition, so they are not implementable on Fock space. Both the…
We revisit the non-perturbative renormalization of a class of simple polaron models with resting fermions. The considered dispersion relations and form factors are allowed to be highly singular, such that infinite self-energies and wave…
We study the partition function $$ Z_n = \int_{\mathbb{C}^n } \prod_{1 \le j<k \le n} |z_{j}-z_{k}|^{2} \prod_{j=1}^{n} |z_j|^{2c}\, e^{-n V(z_{j})}\frac{d^{2}z_{j}}{\pi}, $$ where $c>-1$ and $$ V(z)= |z|^{2d}-t(z^{d}+\overline{z}^{d}),…
We extend the multivariate Fa\`{a} di Bruno formula to the super case, where anticommuting odd coordinates are considered. The formula takes the same form as the classical case but contains some nontrivial signs, which essentially measure…
The exactly solvable Schr\"{o}dinger equations with the conventional shape-invariant potentials are known to be related with each other through point cannonical transformations. In this paper, we extend the idea to integral formulae called…
We have studied the gradient-flow equations in information geometry from a point-particle perspective. Based on the motion of a null (or light-like) particle in a curved space, we have rederived the Hamiltonians which describe the…
Motivated by examples from physics and noncommutative geometry, given a generator $A$ of a Gibbs semigroup, we reexamine the relationship between the Schatten class of its resolvents and the behaviour of the norm-trace $\norm{e^{-tA}}_1\,$…
We study the $\Gamma$-limit of sequences of variational problems for straight, transversely curved shallow shells, as the width of the planform $\varepsilon$ goes to zero. The energy is of von K\'arm\'an type for shallow shells under…
Differential equations need boundary conditions (BC's) for their solution. It is commonly acknowledged that differential equations and BC's are representative of independent physical processes, and no correlations between them is required.…
We study a dilute system of $N$ interacting bosons coupled to an impurity particle via a pair potential in the Gross--Pitaevskii regime. We derive an expansion of the ground state energy up to order one in the boson number, and show that…
Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the…
This paper is a continuation of [1], in which a set of matrix elements of local operators was computed for the XXZ spin-1/2 open chain with a particular case of unparallel boundary fields. Here, we extend these results to the more general…
In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ spin 1/2 chains. We develop our study in the…