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Institute of Physics eBooks

Many-body open systems outside thermodynamic equilibrium

David K. Ferry, Xavier Oriols, Josef Weinbub

Published Nov 1, 2023• 0 citations
Publisher

Abstract

Chapter 3 deals with the general problem of a small device coupled to its environment. Here, we deal with the generality of open quantum systems and with wave function behavior in these devices. We also discuss the extra problems that arise in high-frequency devices.
DOI
10.1088/978-0-7503-5237-6ch3

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The consistent definition of the thermodynamic functions of small open quantum systems in contact with an environment in equilibrium with a heat bath has been the subject of many debates in the quantum community. In the present work we reproduce and comment parts of a recent approach of this subject by Rivas [15]. This approach overcomes the controversial discussions generated by the coupling between a system and its environment for any type of coupling between the two parts and allows for a consistent description of the thermodynamical properties of the system strongly interacting with the bath
We describe in detail a general system–bath strategy for investigating the quantum behavior of small systems interacting with complex environments. In this approach, a simplified heat bath is used as a surrogate for realistic environments, and explicit, unitary quantum simulations of the “universe” (the system plus the bath) are performed by means of high-dimensional wave-packet techniques. In this chapter, we describe the underlying Hamiltonians and the related reduced dynamical descriptions, show how to recast real-world problems into this form, introduce some of the methods currently used to deal with high-dimensional quantum dynamics, and present the results of this strategy when applied to numerous problems of physicochemical interest.
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In the collisional region at finite temperatures, the collective modes of superfluids are described by the Landau two-fluid hydrodynamic equations reviewed in Chapter 14. In the case of trapped Bose gases, these are coupled differential equations with position-dependent coefficients associated with the local thermodynamic functions. Building on the approach initiated by Zaremba et al. (1999) for trapped atomic Bose gases, in this chapter we develop an alternative variational formulation of two-fluid hydrodynamics. This is based on the work of Zilsel (1950), originally developed to deal with superfluid He. Assuming a simple variational ansatz for the superfluid and normal fluid velocity fields, this approach reduces the problem of finding the hydrodynamic collective mode frequencies to solving coupled algebraic equations for a few variational parameters. These equations contain constants that involve spatial integrals over various equilibrium thermodynamic derivatives. Such a variational approach is both simpler and more physical than a direct attempt to solve the Landau two-fluid equations numerically. This chapter is mainly based on Taylor and Griffin (2005), Taylor (2008) and Zilsel (1950). In it, we discuss the normal modes of the non-dissipative Landau two-fluid equations for a trapped superfluid. In Section 16.3, we illustrate this formalism by deriving expressions for the frequencies of the dipole and breathing modes of a trapped Bose superfluid. In Chapters 17 and 18, we discuss an extended version of the two-fluid equations that includes hydrodynamic damping. The hydrodynamic damping of the collective modes is calculated in Chapter 19 using a generalized version of the variational approach developed in this chapter. Zilsel's variational formulation Since two-fluid hydrodynamics only describes a system in local equilibrium, all thermodynamic quantities are functions of position and time. Even in static equilibrium, in the presence of a trapping potential, most thermodynamic quantities will be position dependent.