Related papers: On the BCH formula of Rezek and Kosloff
We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which…
For the Kirillov-Poisson structure on the vector space $\g^*$, where $\g$ is a finite-dimensional Lie algebra, it is known at least two canonical deformations quantization of this structure: they are the M. Kontsevich universal formula [K],…
The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is…
We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is…
We propose a boundary thermodynamic Bethe ansatz calculation technique to obtain the Loschmidt echo and the statistics of the work done when a global quantum quench is performed on an integrable quantum field theory. We derive an analytic…
We discuss the finite-temperature phase diagram in the three-dimensional Bose-Hubbard (BH) model in the strong correlation regime, relevant for Bose-Einstein condensates in optical lattices, by employing a quantum rotor approach. In systems…
In a recent paper we have suggested that the finite temperature density matrix can be computed efficiently by a combination of polynomial expansion and iterative inversion techniques. We present here significant improvements over this…
In this work the Quantum and Statistical Mechanics of the Early Universe, i.e. at Planck scale, is considered as a deformation of the well-known theories. In so doing the primary object under deformation in both cases is the density matrix.…
The general procedure for obtaining explicit expressions for all cohomologies of N.Berkovits's operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern-Simons-like theory (Witten's OSFT-like theory)…
Although all popular approaches to quantum gravity are able to recover the Bekenstein-Hawking entropy-area law in the thermodynamic limit, there are significant differences in their descriptions of the microstates and in the application of…
We consider the heat equation $u_t=Lu$ where $L$ is a second-order difference operator in a discrete variable $n$. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients…
We suggest an algorithm allowing to obtain some new integral-geometric formulae from the existing formulae of Crofton type. These new formulae are applied to get smooth versions of BKK theorem. The algorithm is based on the calculations in…
The atomic movement induced on melting has to overcome a viscous drag resistance. It is suggested that the latent heat of fusion supplies the required energy for this physical process. The viscosity model introduced here allows computation…
I present a brief introduction to the lattice formulation of quantum field theory, and discuss the use of lattice simulations for studies in particle physics phenomenology. The computation of $f_B$, the decay constant of the $B$-meson, is…
Heat engines convert thermal energy into mechanical work both in the classical and quantum regimes. However, quantum theory offers genuine nonclassical forms of energy, different from heat, which so far have not been exploited in cyclic…
Boltzmann solvers are an important tool for the computation of cosmological observables in the linear regime. In the presence of massive neutrinos, they involve solving the Boltzmann equation followed by an integration in momentum space to…
The Besicovitch covering property (BCP) is known to be one of the fundamental tools in measure theory, and more generally, a usefull property for numerous purposes in analysis and geometry. We prove both sufficient and necessary criteria…
Using the Vakarchuk formulae for the density matrix, we calculate the number N_k of atoms with momentum \hbar k for the ground state of a uniform one-dimensional periodic system of interacting bosons. We obtain for impenetrable point bosons…
We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with…
In this paper we develop a gapless theory of BEC which can be applied to both trapped and homogeneous gases at zero and finite temperature. The many-body Hamiltonian for the system is written in a form which is approximately quadratic with…