Related papers: On the BCH formula of Rezek and Kosloff
Bayesian Optimization (BO) has the potential to solve various combinatorial tasks, ranging from materials science to neural architecture search. However, BO requires specialized kernels to effectively model combinatorial domains. Recent…
A microscopic theory for nuclear pairing is proposed through the generalized density matrix formalism. The analytical equations are as simple as that of the BCS theory, and could be solved within a similar computer time. The current theory…
A Bose gas in a double-well potential, exhibiting a true Bose-Einstein condensate (BEC) amplitude and initially performing Josephson oscillations, is a prototype of an isolated, non-equilibrium many-body system. We investigate the…
Following Donaldson's oppenness theorem on deforming a conical K\"ahler-Einstein metric, we prove a parabolic Schauder-type estimate with respect to conical metrics. As a corollary, we show that the conical K\"ahler-Ricci Flow exists for…
The system that describes the dynamics of a Bose-Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB) equations. In such a system of trapped Bose gases…
Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following…
The character change of a superfluid state due to the variation of the attractive force is investigated in the relativistic framework with a massive fermion. Two crossovers are found. One is a crossover from the usual BCS state to the…
We study the Bose-Einstein condensation (BEC) for a relativistic ideal gas of bosons. In the framework of canonical thermal field theory, we analyze the role of particles and anti-particles in the determination of BEC transition…
Out-of-equilibrium phenomena is a subject of considerable interest in many fields of physics. Ultracold quantum gases, which are extremely clean, well-isolated and highly controllable systems, offer ideal platforms to investigate this…
We present a derivation of Boltzmann principle $S_{B}=k_{B}\ln \mathcal{W}$ based on classical mechanical models of thermodynamics. The argument is based on the heat theorem and can be traced back to the second half of the nineteenth…
We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the…
The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, which is proven in the context of the local hidden variable theory, has been used as a test to reveal failure of the hidden variable theory and to prove validity of the quantum theory.…
This article is a pedagogical introduction to the density matrix renormalization group method and its application in quantum chemistry. It presents the easy-to-understand modern formulation based on matrix product states. It is written in…
We propose a BGK-type kinetic model for relativistic reactive gas mixtures. This model serves as a computationally tractable yet physically consistent alternative to the corresponding Boltzmann equation. The relaxation operator is…
We give the thermodynamic definition of the heat magnetization, and calculate with use of the Keldysh formalism in a curved spacetime. The heat magnetization is conjugate to a torsional magnetic field, which is analogous to the fact that…
We establish an effective version of the classical Lie--Kolchin Theorem. Namely, let $A,B\in\mathrm{GL}_m(\mathbb{C})$ be quasi--unipotent matrices such that the Jordan Canonical Form of $B$ consists of a single block, and suppose that for…
In order to close the set of relativistic hydrodynamic equations, constitutive relations for the dissipative fluxes are required. In this work we outline the calculation of the corresponding closure for the heat flux in terms of the…
We solve numerically various types of the gap equations developed in the relativistic BCS and generalized BCS framework, presented in part I of this paper. We apply the method for, not only the usual solid metal but also other physical…
We propose a quantum Stirling heat engine with an ensemble of harmonic oscillators as the working medium. We show that the efficiency of the harmonic oscillator quantum Stirling heat engine (HO-QSHE) at a given frequency can be maximized at…
We study the interior of a Schwarzschild Black-Hole (B-H) using Relativistic Quantum Geometry described in \cite{rb} and \cite{rb1}. We found discrete energy levels for a scalar field from a polynomial condition for Heun Confluent functions…