Effective Dynamics of Disordered Quantum Systems
Author | : Chahan Kropf |
Publisher | : |
Total Pages | : 0 |
Release | : 2017 |
Genre | : |
ISBN | : |
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Author | : Chahan Kropf |
Publisher | : |
Total Pages | : 0 |
Release | : 2017 |
Genre | : |
ISBN | : |
Author | : Chahan Kropf |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Abstract: We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates that encode the specific statistical properties of the Hamiltonian's eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatictest cases
Author | : Bastien Lapierre |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : |
ISBN | : |
Author | : Exner |
Publisher | : Birkhäuser |
Total Pages | : 349 |
Release | : 2013-03-08 |
Genre | : Science |
ISBN | : 3034873069 |
The present volume collects the contributions to the conference "Order, disorder and chaos in quantum systems" which was held at Dubna last October. It is the third meeting in the series started three years ago in which we tried to put together mathematical physicists from the member and non-member countries of JINR with their colleagues from soviet universities and institutes using this international centre as a convenient basis. As in the previous cases, new faces, subj ects and ideas appeared but the spirit remained the same, relaxed and inspirative. Among this conference contributions, a majority should be listed in the "orderly" category. Being more specific, this means mostly various aspects of the theory of Schroedinger operators that has been always a core of quantum mechanics. In spite of the fact that it is studied already for several decades, there are still many interesting problems to solve as some of the lectures collected below witness. At the same time, the theory extends to some new areas motivated by physical problems ; let us mention Schroedinger operators in complicated spatial domains appearing in some parts of solid-state physics or various models using the concept of contact interactions. Our world is far from perfect and to keep a perfect order is difficult not only in everyday life but also in most physical systems. Theoreticians are used to take this fact into account introducing stochastic factors into their considerations.
Author | : Jens Teifel |
Publisher | : |
Total Pages | : 0 |
Release | : 2010 |
Genre | : |
ISBN | : |
Author | : Ofek Asban |
Publisher | : |
Total Pages | : |
Release | : 2021 |
Genre | : |
ISBN | : |
We investigate the dynamics of quantum glasses coupled to a thermal environment via two models, the two-level-system-glass (TG) and the electron-glass (EG). The TG depicts TLSs (pseudo spins) that interact with each other via phonon and/or photon mediated random dipolar interaction. These TLSs represent the dominant degrees of freedom that emerge at low temperatures in amorphous solids. It is argued that the microscopic nature of TLS can be explained by the tunneling of an atom or a group of atoms between two localized nearly degenerate states. The EG depicts electrons that tunnel between localized potential wells and interact via the bare Coulomb interaction. Both TG and EG systems are governed by disorder, thus their excitations are localized and transport is assisted by a bosonic environment at finite temperatures.
Author | : Christopher L. Baldwin |
Publisher | : |
Total Pages | : 132 |
Release | : 2018 |
Genre | : |
ISBN | : |
This thesis concerns the interplay of quantum mechanics with strong disorder, and the novel dynamical phases that are unique to disordered quantum systems. The results that we present apply to systems ranging from spin glasses to granular superconductors to quantum-computational problems. In the first part, we discuss the isolated quantum dynamics of mean-field spin glass models, using the random energy and p-spin models in a transverse field as tractable examples. We show that the low-energy configurations are organized into clusters separated by macroscopic Hamming distances, and that the tunneling amplitudes between clusters are exponentially suppressed. As a result, we find three distinct dynamical phases. At small transverse field, the system remains trapped within its starting cluster (trapped phase). At intermediate transverse field, the system tunnels between clusters (tunneling phase). At large transverse field, the system is excited out of clusters (excitation phase). We describe the similarities and differences between the trapped phase and a many-body localized phase. We also discuss at length the implications for quantum-computational approaches to ``matching'' problems, in which one solution to a computational problem is used as a starting point to find others. Only in the tunneling phase can quantum dynamics solve the matching problem. Although necessarily exponentially slow in system size, it may be exponentially faster than simple classical algorithms. In the second part, we discuss interfering directed paths in disordered media. Important physical realizations are hopping conduction in semiconductors, spin glasses at high temperature, and granular D-wave superconductors. Sign order, defined as the directed path sum having greater probability of being positive than negative at large distance, is a characterization of the role of interference with implications for the response of systems to a magnetic field. We show that path sums are necessarily sign-disordered in two dimensions but may be sign-ordered in three dimensions. Building on this result, we study the behavior of granular D-wave superconductors and show that the superconductivity is enhanced by a magnetic field, even beyond the directed-path regime.
Author | : Baldassare di Bartolo |
Publisher | : Springer Science & Business Media |
Total Pages | : 721 |
Release | : 2006-04-11 |
Genre | : Science |
ISBN | : 0306470802 |
Based on a NATO Advanced Summer Institute, this volume discusses physical models, mathematical formalisms, experimental techniques, and applications for ultrafast dynamics of quantum systems. These systems are used in laser optics, spectroscopy, and utilize monochromaticity, spectral brightness, coherence, power density, and tunability of laser sources.
Author | : Thierry Giamarchi |
Publisher | : Oxford University Press |
Total Pages | : 607 |
Release | : 2016-11-17 |
Genre | : Science |
ISBN | : 0191080535 |
Over the last decade new experimental tools and theoretical concepts are providing new insights into collective nonequilibrium behavior of quantum systems. The exquisite control provided by laser trapping and cooling techniques allows us to observe the behavior of condensed bose and degenerate Fermi gases under nonequilibrium drive or after `quenches' in which a Hamiltonian parameter is suddenly or slowly changed. On the solid state front, high intensity short-time pulses and fast (femtosecond) probes allow solids to be put into highly excited states and probed before relaxation and dissipation occur. Experimental developments are matched by progress in theoretical techniques ranging from exact solutions of strongly interacting nonequilibrium models to new approaches to nonequilibrium numerics. The summer school `Strongly interacting quantum systems out of equilibrium' held at the Les Houches School of Physics as its XCIX session was designed to summarize this progress, lay out the open questions and define directions for future work. This books collects the lecture notes of the main courses given in this summer school.
Author | : Mattia Walschaers |
Publisher | : Springer |
Total Pages | : 450 |
Release | : 2018-07-31 |
Genre | : Science |
ISBN | : 3319931512 |
This book introduces a variety of statistical tools for characterising and designing the dynamical features of complex quantum systems. These tools are applied in the contexts of energy transfer in photosynthesis, and boson sampling. In dynamical quantum systems, complexity typically manifests itself via the interference of a rapidly growing number of paths that connect the initial and final states. The book presents the language of graphs and networks, providing a useful framework to discuss such scenarios and explore the rich phenomenology of transport phenomena. As the complexity increases, deterministic approaches rapidly become intractable, which leaves statistics as a viable alternative.