Effect of Thermal Fluctuations on Classical and Quantum Systems at Small Scales

A. Mann, M. Revzen, Hiroomi Umezawa +1 more

Aravind Panneerselvam

The area of quantum thermodynamics is a relatively new field and there are great efforts in research to study the effects of microscopic work, heat, efficiency and other associated properties due to its vast potential applications in micro engineering and biophysics. The transition from large scale classical macro systems to small scale micro systems is not straightforward and the effects of different properties pose different responses in the system. As the systems miniaturise large scale fluctuations that in classical thermodynamics were once neglected, become of great importance in micro systems. In this thesis, a review of the current understandings of quantum thermodynamics is given with particular interest in Carnot engines and the maximum efficiency proposed by Curzon-Ahlborn. From a quantum analog of the Carnot engine, found in previous studies, the effects of thermal variations were investigated and the resulting response of the systems shows correlation to classical Carnot engines. It was found that increasing thermal fluctuations result in a decrease in maximum efficiency. Furthermore, to optimise these engines decreasing thermal fluctuations is necessary in order to build quantum engines that can trend towards or potentially reach the maximum Carnot efficiency.

Pierfrancesco Urbani

Abstract Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.

Andreas Glatz

Mark Srednicki

We consider a quantum system with N degrees of freedom which is classically chaotic. When N is large, and both and the quantum energy uncertainty are small, quantum chaos theory can be used to demonstrate the following results: (i) given a generic observable A, the infinite time average of the quantum expectation value is independent of all aspects of the initial state other than the total energy, and equal to an appropriate thermal average of A; (ii) the time variations of are too small to represent thermal fluctuations; (iii) however, the time variations of can be consistently interpreted as thermal fluctuations, even though these same time variations would be called quantum fluctuations when N is small.

Neha Pathania, Devvrat Tiwari, Subhashish Banerjee