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The European Physical Journal Special Topics

A Boltzmann equation approach to transport in finite modular quantum systems

Mehmet Kadiroḡlu, Jochen Gemmer B

Published Dec 1, 2007• 0 citations
Publisher
DOI
10.1140/epjst/e2007-00368-3

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BTELab, a MATLAB Programme Code for solving Quantum Boltzmann Transport Equation with all Collision Terms within Trapping Potential

Sunipa Som, Ravindra Dhar, Ram Kripal +1 more

Abstract This paper presents Quantum Boltzmann Transport Equation Laboratory (QBTELab), an advanced easy-to-use toolbox to solve many complex problems related to Bose-Einstein Condensate (BEC). The model equation that BTELab solves is the Quantum Boltzmann Transport Equation (QBTE) with all collision terms within trapping potential. Inelastic scattering (Exciton-phonon collision), elastic scattering (exciton-exciton collision), Auger decay and radiative non-radiative decay are included here as the collision terms. The programme code has been written in MATLAB. From the results it can be said that the programme is working properly and it has enough numerical stability. The aim of this paper is to provide programme code to solve the full QBTE. QBTE is a powerful tool for investigating the transport phenomena in various systems like semiconductors, plasmas, nuclear reactors, heat transfer process, fluid dynamics etc and specially different problems related to BEC.

•Oct 9, 2026•0 citations
We investigate the transport behavior of finite modular quantum systems. Such systems have recently been analyzed by different methods. These approaches indicate diffusive behavior even, and especially, for finite systems. Inspired by these results we analytically and numerically analyze if and in which sense the dynamics of those systems are in agreement with an appropriate Boltzmann equation. We find that the transport behavior of a certain type of finite modular quantum systems may indeed be described in terms of a Boltzmann equation. However, the applicability of the Boltzmann equation appears to be rather limited to a very specific type of model.
A bstract We study the quantum transport generated by the bipartite entanglement in two-dimensional conformal field theory at finite density with the U(1) × U(1) symmetry associated to the conservation of the electric charge and of the helicity. The bipartition given by an interval is considered, either on the line or on the circle. The continuity equations and the corresponding conserved quantities for the modular flows of the currents and of the energy-momentum tensor are derived. We investigate the mean values of the associated currents and their quantum fluctuations in the finite density representation, which describe the properties of the modular quantum transport. The modular analogues of the Johnson- Nyquist law and of the fluctuation-dissipation relation are found, which encode the thermal nature of the modular evolution.
Abstract This paper presents Quantum Boltzmann Transport Equation Laboratory (QBTELab), an advanced easy-to-use toolbox to solve many complex problems related to Bose-Einstein Condensate (BEC). The model equation that BTELab solves is the Quantum Boltzmann Transport Equation (QBTE) with all collision terms within trapping potential. Inelastic scattering (Exciton-phonon collision), elastic scattering (exciton-exciton collision), Auger decay and radiative non-radiative decay are included here as the collision terms. The programme code has been written in MATLAB. From the results it can be said that the programme is working properly and it has enough numerical stability. The aim of this paper is to provide programme code to solve the full QBTE. QBTE is a powerful tool for investigating the transport phenomena in various systems like semiconductors, plasmas, nuclear reactors, heat transfer process, fluid dynamics etc and specially different problems related to BEC.