Related papers: Time-dependent correlation function of the Jordan-…

In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevancy of the fermionic picture for interpreting the neutron scattering…

Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the…

The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equations. Their methods are based on the theory of integrable…

We generalize the winding number formula for the Fredholm index of a Toeplitz operator to the Witten index. We also show trace formulae involving Toeplitz operators and operator monotone functions.

The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the…

Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the…

The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein--Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the…

This paper concerns Fredholm theory in several variables, and its applications to Hilbert spaces of analytic functions. One feature is the introduction of ideas from commutative algebra to operator theory. Specifically, we introduce a…

The Macdonald process is a stochastic process on the collection of partitions that is a $(q,t)$-deformed generalization of the Schur process. In this paper, we approach the Macdonald process identifying the space of symmetric functions with…

We study models of quantum statistical mechanics which can be solved by the algebraic Bethe ansatz. The general method of calculation of correlation functions is based on the method of determinant representations. The auxiliary Fock space…

In this paper we shall focus on one-dimensional strictly local operators, the notion of which naturally arises in the context of discrete-time quantum walks on the one-dimensional integer lattice. In particular, we give an elementary…

We give an elementary derivation of the vertex-operator derivation McMahon formula, counting all plane partitions of all size into a single generating function. We fill in some details appearing in Okounkov, Reshetikhin, and Vafa based on…

The main goal of this paper is to put on solid mathematical grounds the so-called Non-Equilibrium Green's Function (NEGF) transport formalism for open systems. In particular, we derive the Jauho-Meir-Wingreen formula for the time-dependent…

Coupled Maxwell and time-dependent orbital-free calculations are implemented and tested to describe the interaction of electromagnetic waves and matter. The currents and induced fields predicted by the orbital-free calculations are compared…

We consider a general statistical inference model of finite-rank tensor products. For any interaction structure and any order of tensor products, we identify the limit free energy of the model in terms of a variational formula. Our approach…

An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…

Recently a Jordan-Wigner transformation was constructed for spinful fermions at S=1/2 spins in one dimension connecting the spin-1/2 operators to genuine spinful canonical Fermi operators. In the presented paper this exact transformation is…

We will establish the connection between the Lorentz covariant and so-called single-time formulation for the quark Wigner operator. To this end we will discuss the initial value problem for the Wigner operator of a field theory and give a…

We study various spectral theoretic aspects of non-self-adjoint operators. Specifically, we consider a class of factorable non-self-adjoint perturbations of a given unperturbed non-self-adjoint operator and provide an in-depth study of a…