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Journal of Physics Conference Series

Dissipative quantum dynamics

Leticia F. Cugliandolo

Published Jan 7, 2009• 1 citation
Publisher

Abstract

This article reviews recent research on dissipative macroscopic quantum bosonic and fermionic systems. These studies address the following issues. (i) The existence of static and dynamic phase transitions; order of the critical lines and type of phases. (ii) The dynamics of systems that are unable to reach equilibrium with their (equilibrium) environment due to their intrinsic slow dynamics or driven by an external drive in the form of a time-dependent magnetic field, coupling to source and drain leads, etc. (iii) The development of an effective temperature that controls the large-scale dynamics and a two-time dependent decoherence phenomenon. (iv) The role played by the environment in the behaviour of the systems.

DOI
10.1088/1742-6596/143/1/012006

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This article reviews recent research on dissipative macroscopic quantum bosonic and fermionic systems. These studies address the following issues. (i) The existence of static and dynamic phase transitions; order of the critical lines and type of phases. (ii) The dynamics of systems that are unable to reach equilibrium with their (equilibrium) environment due to their intrinsic slow dynamics or driven by an external drive in the form of a time-dependent magnetic field, coupling to source and drain leads, etc. (iii) The development of an effective temperature that controls the large-scale dynamics and a two-time dependent decoherence phenomenon. (iv) The role played by the environment in the behaviour of the systems.
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered -- glassy -- phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random Ising chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and how they compare to the behaviour of the same models in their classical limit. (ii) The phase transition separating the ordered – glassy – phase from the disordered phase that, for some long-range interactions, is of second order at high temperatures and of first order close to the quantum critical point (similarly to what has been observed in random dipolar magnets). (iii) The static properties of the Griffiths phase in random king chains. (iv) The dependence of all these properties on the environment. The analytic and numeric techniques used to derive these results are briefly mentioned.
Quantum dissipation has been the object of study within the physics and chemistry communities for many years. Despite this, the field is in constant evolution, largely due to the fact that novel systems where the understanding of dissipation and dephasing processes is of crucial importance have become experimentally accessible in recent years. Among the ongoing research themes, we mention the defeat of decoherence in solid state-based quantum bits (qubits) (e.g. superconducting qubits or quantum dot based qubits), or dissipation due to non-equilibrium Fermi reservoirs, as is the case for quantum transport through meso- and nanoscale structures. A close inspection of dissipation in such systems reveals that one has to deal with 'unconventional' environments, where common assumptions of, for example, linearity of the bath and/or equilibrium reservoir have to be abandoned. Even for linear baths at equilibrium it might occur that the bath presents some internal structure, due, for example, to the presence of localized bath modes. A large part of this focus issue is devoted to topics related to the rapidly developing fields of quantum computation and information with solid state nanodevices. In these implementations, single and two-qubit gates as well as quantum information transmission takes place in the presence of broadband noise that is typically non-Markovian and nonlinear. On both the experimental and theory side, understanding and defeating such noise sources has become a crucial step towards the implementation of efficient nanodevices. On a more fundamental level, electron and spin transport through quantum dot nanostructures may suffer from 'unconventional' dissipation mechanisms such as the simultaneous presence of spin relaxation and fermionic dissipation, or may represent themselves out of equilibrium baths for nearby mesoscopic systems. Finally, although not expected from the outset, the present collection of articles has revealed that different 'unconventional' questions were still open on the standard harmonic oscillator and spin baths. This includes both fundamental issues, such as the possibility of estimating the specific heat for a free particle in the presence of dissipation, and the development of methods suitable to dealing with long range correlations at zero temperature and with quantum chaotic environments. We believe that the present focus issue on Quantum Dissipation in Unconventional Environments , although certainly not exhaustive, provides an important open-access resource that presents the latest state of the art of research in this field along its different lines. Focus on Quantum Dissipation in Unconventional Environments Contents Coherent control of an effective two-level system in a non-Markovian biomolecular environment J Eckel, J H Reina and M Thorwart Charge transfer dynamics in driven molecular ratchets: quantum Monte Carlo results and rate models L Mühlbacher and J Ankerhold Decoherence in qubits due to low-frequency noise J Bergli, Y M Galperin and B L Altshuler Dephasing by electron–electron interactions in a ballistic Mach–Zehnder interferometer Clemens Neuenhahn and Florian Marquardt Quantum frustration of dissipation by a spin bath D D Bhaktavatsala Rao, Heiner Kohler and Fernando Sols A random matrix theory of decoherence T Gorin, C Pineda, H Kohler and T H Seligman Dissipative dynamics of a biased qubit coupled to a harmonic oscillator: analytical results beyond the rotating wave approximation Johannes Hausinger and Milena Grifoni Dissipative dynamics of a two-level system resonantly coupled to a harmonic mode Frederico Brito and Amir O Caldeira Spin correlations in spin blockade Rafael Sánchez, Sigmund Kohler and Gloria Platero Landau–Zener tunnelling in dissipative circuit QED David Zueco, Peter Hänggi and Sigmund Kohler Quantum oscillations in the spin-boson model: reduced visibility from non-Markovian effects and initial entanglement F K Wilhelm Dynamics of dissipative coupled spins: decoherence, relaxation and effects of a spin-boson bath P Nägele, G Campagnano and U Weiss Spin chain model for correlated quantum channels Davide Rossini, Vittorio Giovannetti and Simone Montangero Finite quantum dissipation: the challenge of obtaining specific heat Peter Hänggi, Gert-Ludwig Ingold and Peter Talkner Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition Frithjof B Anders Effects of low-frequency noise cross-correlations in coupled superconducting qubits A D'Arrigo, A Mastellone, E Paladino and G Falci From coherent motion to localization: dynamics of the spin-boson model at zero temperature Haobin Wang and Michael Thoss Phonon distributions of a single-bath mode coupled to a quantum dot F Cavaliere, G Piovano, E Paladino and M Sassetti
All real-world quantum systems interact with their surrounding environment to some extent. No matter how weak the coupling that prevents the system from being isolated, the evolution of an open quantum system is eventually plagued by non-unitary features, such as decoherence and dissipation. Decoherence is a quantum effect where the system loses its ability to exhibit coherent behavior. Nowadays, decoherence stands as a serious obstacle in quantum information processing. As the manipulation of quantum coherence in experiments has progressed, the need to better understand, control, and utilize dissipative non-equilibrium dynamics of quantum systems has grown in importance. This has ranged from fundamental questions associated with the quantum-to-classical transition and quantum thermodynamics innovation in quantum optics and cavity/circuit quantum electrodynamics. Current studies of many-body dynamics, ultracold atoms in optical lattices, trapped ions, superconducting systems, nanoelectro-mechanical systems, and quantum fields under the influence of external conditions offer new challenges to address questions regarding quantum systems far from equilibrium. On the theoretical side, quantum trajectory-based methods could be the key to both quantum nanodevice design and exploration of new regimes of quantum mechanics and quantum measurement, as well as applications to various quantum technologies.
We analyze the out-of-equilibrium relaxational dynamics of ferromagnetic Ising-like systems driven across their low-temperature magnetic first-order transition (FOT) line, by sudden and slow variations of an external homogenous magnetic field hhh. As a paradigmatic example, we consider a two-dimensional Ising system driven across its low-temperature FOT line by suddently quenching hhh from hi<0h_i<0hi​<0 to h>0h>0h>0, inducing a transition from the negatively to the positively magnetized phase. We show the emergence of a dynamic percolation transition at a finite critical time tc(h)t_c(h)tc​(h) along the post-quench evolution for finite (sufficiently small) values of hhh, which is marked by the percolation of the largest positive-spin cluster and the antipercolation of the largest negative-spin cluster. This out-of-equilibrium percolation transition displays a finite-size scaling behavior as in the standard random-percolation case. However, while the fractal dimension of the percolating clusters is consistent with the random-percolation value, the exponent controlling the approach to criticality differs and depends on hhh. We also show that the percolation transition marks the passage from the metastable negatively-magnetized phase to the stable positively-magnetized one. Therefore, in the small-hhh limit, the percolation critical behavior is related to the spinodal-like behavior of the magnetization, implying that the percolation time tc(h)t_c(h)tc​(h) exhibits a spinodal-like exponential dependence on hhh. The existence of percolation transitions is likely a generic phenomenon at magnetic Ising-like FOTs. For example, we observe an analogous behavior in dynamic (Kibble-Zurek-like) protocols entailing slow variations of the magnetic field driving the crossing of the FOT line.