Related papers: A New Determinant for Quantum Chaos
The six-vertex model with domain wall boundary conditions is considered. A Fredholm determinant representation for the partition function of the model is obtained. The kernel of the corrtesponding integral operator depends on Laguerre…
Let $(-A,B,C)$ be a continuous time linear system with state space a separable complex Hilbert space $H$, where $-A$ generates a strongly continuous contraction semigroup $(e^{-tA})_{t\geq 0}$ on $H$, and $\phi (t)=Ce^{-tA}B$ is the impulse…
We study the inner product of two Bethe states, one of which is taken on-shell, in an inhomogeneous XXX chain in the Sutherland limit, where the number of magnons is comparable with the length L of the chain and the magnon rapidities…
An important problem in applications of quasiconformal analysis and in its numerical aspect is to establish algorithms for explicit or approximate determination of the basic quasiinvariant curvelinear and analytic functionals intrinsically…
On a compact manifold $M$, we consider the affine space $A$ of non self-adjoint perturbations of some invertible elliptic operator acting on sections of some Hermitian bundle, by some differential operator of lower order. We construct and…
Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distribution in…
We undertake an analysis of Fredholm determinants arising from kernels whose defining functions satisfy a Schr\"odinger type equation. When this defining function is the Airy one, the evaluation of the corresponding Fredholm determinant…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
A classical problem in operator theory has been to determine the spectrum of Toeplitz-like operators on Hilbert spaces of vector-valued holomorphic functions on the open unit ball in C^m. In this note we obtain necessary conditions for…
We consider the quantum tunneling phenomenon in a well-behaved triple-well potential. As required by the semiclassical approximation we take into account the quadratic fluctuations over the instanton which represents as usual the localised…
Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in…
We investigate the simplest class of hyperdeterminants defined by Cayley in the case of Hankel hypermatrices (tensors of the form $A_{i_1i_2... i_k}=f(i_1+i_2+...+i_k)$). It is found that many classical properties of Hankel determinants can…
Let $\bigwedge_\sigma V=\bigoplus_{k\geq 0}\bigwedge_\sigma^kV$ be the quantum exterior algebra associated to a finite-dimensional braided vector space $(V,\sigma)$. For an algebra $\mathfrak{A}$, we consider the convolution product on the…
We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…
This paper concerns hyperbolic systems of two linear first-order PDEs in one space dimension with periodicity conditions in time and reflection boundary conditions in space. The coefficients of the PDEs are supposed to be time independent,…
For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim(N\ge1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the…
It has been known since the pioneering paper of Mark Kac, that the asymptotics of Fredholm determinants can be studied using probabilistic methods. We demonstrate the efficacy of Kac' approach by studying the Fredholm Pfaffian describing…
We develop a pseudodifferential calculus for differential operators associated to quasi-fibered boundary metrics (QFB metrics), a class of metrics including the quasi-asymptotically conical metrics (QAC metrics) of Degeratu-Mazzeo and the…
In 1970s Segal outlined proofs of two theorems relating spaces of Fredholm and self-adjoint Fredholm operators with Quillen's constructions used to define higher algebraic K-theory. In the present paper we provide detailed proofs of these…
We compute the quantized Hall conductance at various Landau levels by using the classic trace. The computations reduce to the single elementary one for the lowest Landau level. By using the theories of Helton-Howe-Carey-Pincus, and Toeplitz…