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arXiv:0909.2316

Quantum Phase Transition, Dissipation, and Measurement

Sudip Chakravarty

Published Sep 12, 2009• 0 citations
arXivHTMLPDF

Abstract

A selected set of topics in quantum phase transition is discussed. It includes dissipative quantum phase transitions, the role of disorder, and the relevance of quantum phase transition to measurement theory in quantum mechanics.
DOI
10.48550/arxiv.0909.2316

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Sudip Chakravarty Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095-1547, U.S.A. This chapter reflects my subjective choice of topics. My interest falls into three distinct categories. The intense interest in the problem of dissipation in quantum systems began at the time when macroscopic quantum tunneling and coherence in superconducting quantum interference devices (SQUIDs) were proposed. This subject has seen considerable developments over the past three decades both in theory and in experiments [1]. An important problem in this subject is a particle in a double well potential coupled to a bath consisting of an infinite number of harmonic oscillators providing a linear dissipation to the particle, in other words coupled to an Ohmic heat bath in the language of electrical engineering [2]. Yet, it is hardly recognized that this problem constitutes one of the simplest models of quantum criticality [3]. Thus, unsurprisingly, little attention has been paid over the years to experimentally explore this critical phenomenon. It remains equally unrecognized that the same model holds a germ of the quantum-to-classical transition much discussed in measurement theory.1 Here I have attempted to draw a parallel with an even more elementary model of Coleman and Hepp [4], which actually contains no dissipation. Nonetheless the two problems are united by the dictum that for infinitely many degrees of freedom two distinct states of matter cannot be unitarily related. A particle in a double well coupled to a dissipative environment is indeed a system with an infinite number of degrees of freedom. Of course, the Coleman-Hepp model can be supplemented by dissipation to bring the two models closer, but the basic issue with respect to measurement is clearer in its original form.

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Sudip Chakravarty Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, CA 90095-1547, U.S.A. This chapter reflects my subjective choice of topics. My interest falls into three distinct categories. The intense interest in the problem of dissipation in quantum systems began at the time when macroscopic quantum tunneling and coherence in superconducting quantum interference devices (SQUIDs) were proposed. This subject has seen considerable developments over the past three decades both in theory and in experiments [1]. An important problem in this subject is a particle in a double well potential coupled to a bath consisting of an infinite number of harmonic oscillators providing a linear dissipation to the particle, in other words coupled to an Ohmic heat bath in the language of electrical engineering [2]. Yet, it is hardly recognized that this problem constitutes one of the simplest models of quantum criticality [3]. Thus, unsurprisingly, little attention has been paid over the years to experimentally explore this critical phenomenon. It remains equally unrecognized that the same model holds a germ of the quantum-to-classical transition much discussed in measurement theory.1 Here I have attempted to draw a parallel with an even more elementary model of Coleman and Hepp [4], which actually contains no dissipation. Nonetheless the two problems are united by the dictum that for infinitely many degrees of freedom two distinct states of matter cannot be unitarily related. A particle in a double well coupled to a dissipative environment is indeed a system with an infinite number of degrees of freedom. Of course, the Coleman-Hepp model can be supplemented by dissipation to bring the two models closer, but the basic issue with respect to measurement is clearer in its original form.