Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings from the institute for nuclear theory

Tunneling in Complex Systems

Steven Tomsovic

Published Jun 1, 1998• 43 citations
Publisher

Abstract

Some general aspects of quantum tunnelling and coherence - application to the BEC atomic gases, A.J. Leggett tunnelling in two-dimensions, S.C. Creagh quantum environments - spin baths, oscillator baths and applications to quantum magnetism, P. Stamp coherent magnetic moment reversal in small particles with nuclear spins, A. Garg tunnelling from super- to normal-deformed minima in nuclei, T.L. Khoo solitons in the bose condensate, W.P. Reinhardt.

DOI
10.1142/3768

Related papers

Theory of the spin bath

Nikolay V. Prokof'ev, Philip C. E. Stamp

The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many `environmental' modes. At low T these environmental effects are dominated by localized modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a `spin bath' model. This contrasts with `oscillator bath' models (originated by Feynman and Vernon) which describe delocalized environmental modes such as electrons, phonons, photons, magnons, etc. The couplings to N spin bath modes are independent of N (rather than the ~O(1/( N ) 1/2 ) dependence typical of oscillator baths), and often strong. One cannot in general map a spin bath to an oscillator bath (or vice versa); they constitute distinct `universality classes' of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We then focus on the `central spin' model, which couples a central two-level system to a background spin bath. It is the spin bath analogue of the famous `spin-boson' oscillator model, and describes, e.g., the tunnelling dynamics of nanoscopic and mesoscopic magnets and superconductors. We show how to average over (or `integrate out') spin bath modes, using an operator instanton technique, to find the central spin dynamics. The formal manouevres involve four separate averages - each average corresponds physically to a different `decoherence' mechanism acting on the central spin dynamics. Each environmental spin has its own topological `spin phase', which by interacting with the phase of the central system, decoheres it - this can happen even without dissipation. We give analytic results for the central spin correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems. Particular attention is given to recent work on tunnelling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunnelling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs. Finally, we discuss decoherence mechanisms and coherence experiments in superconductors and magnets. We show that a spin bath environment causes decoherence even in the T 0 limit. Control of this decoherence will be essential in the effort to construct `qubits' for quantum computers.

arXiv:cond-mat/0001080•Reports on Progress in Physics•Mar 22, 2000•538 citations

Chapter 25: Some Examples of Quantum Tunneling in Atomic and Molecular Physics

WORLD SCIENTIFIC eBooks•Jan 14, 2014•0 citations

Oscillator bath simulation of the spin bath

Seyyed M. H. Halataei

Open quantum systems are subject to interaction with their surrounding environment. In many applications, at low temperatures, quantum environments fall into two universality classes of models: Caldeira-Leggett oscillator bath models and Prokof'ev-Stamp spin bath models. The two classes are commonly recognized to be distinct and to have strikingly different effects on principal systems, except at weak coupling limits. However, I show here, in contrast, that oscillator bath models can simulate the effect of spin bath models in strong coupling limit of the spin bath. I choose parameters of the oscillator bath models such that they produce incoherent relaxation, just as in the spin bath models, with relaxation rates for a two-state system (a qubit) equivalent to those of the spin bath models in the strong coupling limit.

arXiv:1703.04592•Mar 14, 2017•0 citations

SOME GENERAL ASPECTS OF QUANTUM TUNNELING AND COHERENCE: APPLICATION TO THE BEC ATOMIC GASES

A. J. Leggett

Proceedings from the institute for nuclear theory•Jun 1, 1998•0 citations

Quantum behaviour of molecule-based magnets: basic aspects (quantum tunneling and quantum coherence) and applications (hardware for quantum computers and magnetic refrigeration). A tutorial

Javier Tejada

Polyhedron•May 1, 2001•32 citations

Caldeira-Leggett oscillator bath simulation of the Prokof'ev-Stamp spin bath in strong coupling limits

Seyyed M. H. Halataei

Open quantum systems are subject to interaction with their surrounding environments. The environments are in general complex and intractable. At low temperatures, quantum environments are mapped onto two simpler universality classes of models, namely oscillator bath and spin bath models. The two models are commonly recognized as completely distinct at strong coupling limits. In particular, it is believed, that they cause two different dissipative relaxation rates when they act on qubits. It is also believed that at such a limit the relaxation rate caused by the spin bath model cannot be simulated by the oscillator bath model. In this paper, I show, in contrast, that the oscillator bath model can simulate the effect of the spin bath model in the strong coupling limit of the spin bath. I demonstrate that, by choosing the right parameters for the oscillator bath model such that it induces the same rate and amount of bias energy fluctuations as those of the spin bath, the oscillator bath model can produce a relaxation rate equivalent to that of the spin bath model. This result implies that, as far as the relaxation rate is concerned, the distinction between the oscillator bath model and the spin bath model is far less than has been previously recognized.

arXiv:2108.04915•Aug 10, 2021•0 citations
Some general aspects of quantum tunnelling and coherence - application to the BEC atomic gases, A.J. Leggett tunnelling in two-dimensions, S.C. Creagh quantum environments - spin baths, oscillator baths and applications to quantum magnetism, P. Stamp coherent magnetic moment reversal in small particles with nuclear spins, A. Garg tunnelling from super- to normal-deformed minima in nuclei, T.L. Khoo solitons in the bose condensate, W.P. Reinhardt.
The quantum dynamics of mesoscopic or macroscopic systems is always complicated by their coupling to many `environmental' modes. At low T these environmental effects are dominated by localized modes, such as nuclear and paramagnetic spins, and defects (which also dominate the entropy and specific heat). This environment, at low energies, maps onto a `spin bath' model. This contrasts with `oscillator bath' models (originated by Feynman and Vernon) which describe delocalized environmental modes such as electrons, phonons, photons, magnons, etc. The couplings to N spin bath modes are independent of N (rather than the ~O(1/( N ) 1/2 ) dependence typical of oscillator baths), and often strong. One cannot in general map a spin bath to an oscillator bath (or vice versa); they constitute distinct `universality classes' of quantum environment. We show how the mapping to spin bath models is made, and then discuss several examples in detail, including moving particles, magnetic solitons, nanomagnets, and SQUIDs, coupled to nuclear and paramagnetic spin environments. We then focus on the `central spin' model, which couples a central two-level system to a background spin bath. It is the spin bath analogue of the famous `spin-boson' oscillator model, and describes, e.g., the tunnelling dynamics of nanoscopic and mesoscopic magnets and superconductors. We show how to average over (or `integrate out') spin bath modes, using an operator instanton technique, to find the central spin dynamics. The formal manouevres involve four separate averages - each average corresponds physically to a different `decoherence' mechanism acting on the central spin dynamics. Each environmental spin has its own topological `spin phase', which by interacting with the phase of the central system, decoheres it - this can happen even without dissipation. We give analytic results for the central spin correlation functions, under various conditions. We then describe the application of this theory to magnetic and superconducting systems. Particular attention is given to recent work on tunnelling magnetic macromolecules, where the role of the nuclear spin bath in controlling the tunnelling is very clear; we also discuss other magnetic systems in the quantum regime, and the influence of nuclear and paramagnetic spins on flux dynamics in SQUIDs. Finally, we discuss decoherence mechanisms and coherence experiments in superconductors and magnets. We show that a spin bath environment causes decoherence even in the T 0 limit. Control of this decoherence will be essential in the effort to construct `qubits' for quantum computers.
Open quantum systems are subject to interaction with their surrounding environment. In many applications, at low temperatures, quantum environments fall into two universality classes of models: Caldeira-Leggett oscillator bath models and Prokof'ev-Stamp spin bath models. The two classes are commonly recognized to be distinct and to have strikingly different effects on principal systems, except at weak coupling limits. However, I show here, in contrast, that oscillator bath models can simulate the effect of spin bath models in strong coupling limit of the spin bath. I choose parameters of the oscillator bath models such that they produce incoherent relaxation, just as in the spin bath models, with relaxation rates for a two-state system (a qubit) equivalent to those of the spin bath models in the strong coupling limit.
Open quantum systems are subject to interaction with their surrounding environments. The environments are in general complex and intractable. At low temperatures, quantum environments are mapped onto two simpler universality classes of models, namely oscillator bath and spin bath models. The two models are commonly recognized as completely distinct at strong coupling limits. In particular, it is believed, that they cause two different dissipative relaxation rates when they act on qubits. It is also believed that at such a limit the relaxation rate caused by the spin bath model cannot be simulated by the oscillator bath model. In this paper, I show, in contrast, that the oscillator bath model can simulate the effect of the spin bath model in the strong coupling limit of the spin bath. I demonstrate that, by choosing the right parameters for the oscillator bath model such that it induces the same rate and amount of bias energy fluctuations as those of the spin bath, the oscillator bath model can produce a relaxation rate equivalent to that of the spin bath model. This result implies that, as far as the relaxation rate is concerned, the distinction between the oscillator bath model and the spin bath model is far less than has been previously recognized.