7. Dissipation and the Dynamics of Macroscopic Quantum Systems

We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it causes destructive interference to suppress the quantum fluctuation. Using the variational method, we confirm that this dissipation term is a reasonable extension of the standard (Schrödinger) description for isolated systems, from which we also derive the classical action. Consequently, in macroscopic systems, the states whose time-integrated dissipation takes an extreme value come true. This description, which is consistent with our sense of reality, coexists with the usual linear-time-dependent description.We study the connection between dissipation and reality in macroscopic quantum systems. We present the following scenario; if we consider the dynamics of a `partial' wave function, the dissipation is represented as a nonlocal term and it causes destructive interference to suppress the quantum fluctuation. Using the variational method, we confirm that this dissipation term is a reasonable extension of the standard (Schrödinger) description for isolated systems, from which we also derive the classical action. Consequently, in macroscopic systems, the states whose time-integrated dissipation takes an extreme value come true. This description, which is consistent with our sense of reality, coexists with the usual linear-time-dependent description.

arXiv:quant-ph/0703002Mar 1, 20070 citations

Macroscopic Quantum Coherence and Dissipation

Andrei D. Zaikin, Dmitry S. Golubev

This chapter describes the analysis of the effect of dissipation on quantum properties of double-well systems. The simple qualitative observation suggests that interaction with a dissipative bath can significantly alter physical properties of a quantum mechanical particle in a double-well potential. The chapter provides the description of real-time dynamics of the double-well systems in the presence of linear Ohmic dissipation. It shows that dissipation yields total loss of coherence and, hence, real-time dynamics of the system remains incoherent at all times. Drastic simplifications occur if one assumes that the average time the system remains in a state described by the diagonal density matrix strongly exceeds the time it spends in the off-diagonal state. The collective charge variable is canonically conjugate to that of the phase, thus also describing quantum states of a macroscopically large number of electron degrees of freedom.This chapter describes the analysis of the effect of dissipation on quantum properties of double-well systems. The simple qualitative observation suggests that interaction with a dissipative bath can significantly alter physical properties of a quantum mechanical particle in a double-well potential. The chapter provides the description of real-time dynamics of the double-well systems in the presence of linear Ohmic dissipation. It shows that dissipation yields total loss of coherence and, hence, real-time dynamics of the system remains incoherent at all times. Drastic simplifications occur if one assumes that the average time the system remains in a state described by the diagonal density matrix strongly exceeds the time it spends in the off-diagonal state. The collective charge variable is canonically conjugate to that of the phase, thus also describing quantum states of a macroscopically large number of electron degrees of freedom.

May 24, 20190 citations

Incorporating Dissipation in Quantum Dynamics

Alberto Acevedo, Manuel Berrondo, Jean-François S. Van Huele

Bulletin of the American Physical SocietyOct 18, 20140 citations

Photoinduced macroscopic quantum tunneling

Sudip Chakravarty, Steven Allan Kivelson

Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/ ${e}^{2}$ . .AERecently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/${e}^{2}$. .AE

Physical review. B, Condensed matterJul 1, 198546 citations

{e}^{2}

. .AE