The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform
Michael J Hartmann - One of the best experts on this subject based on the ideXlab platform.
-
self consistent Projection Operator theory in nonlinear quantum optical systems a case study on degenerate optical parametric oscillators
Physical Review A, 2015Co-Authors: Peter Degenfeldschonburg, Carlos Navarretebenlloch, Michael J HartmannAbstract:Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent Projection Operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
-
self consistent Projection Operator theory in nonlinear quantum optical systems a case study on degenerate optical parametric oscillators
Physical Review A, 2015Co-Authors: Peter Degenfeldschonburg, Carlos Navarretebenlloch, Michael J HartmannAbstract:Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent Projection Operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
-
self consistent Projection Operator theory for quantum many body systems
Physical Review B, 2014Co-Authors: Peter Degenfeldschonburg, Michael J HartmannAbstract:We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our Projection Operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides a novel interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of non-equilibrium states in closed and stationary states in driven-dissipative systems.
-
self consistent Projection Operator theory for quantum many body systems
Physical Review B, 2014Co-Authors: Peter Degenfeldschonburg, Michael J HartmannAbstract:We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our Projection Operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides an interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of nonequilibrium states in closed and stationary states in driven-dissipative systems.
Peter Degenfeldschonburg - One of the best experts on this subject based on the ideXlab platform.
-
self consistent Projection Operator theory in nonlinear quantum optical systems a case study on degenerate optical parametric oscillators
Physical Review A, 2015Co-Authors: Peter Degenfeldschonburg, Carlos Navarretebenlloch, Michael J HartmannAbstract:Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent Projection Operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
-
self consistent Projection Operator theory in nonlinear quantum optical systems a case study on degenerate optical parametric oscillators
Physical Review A, 2015Co-Authors: Peter Degenfeldschonburg, Carlos Navarretebenlloch, Michael J HartmannAbstract:Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent Projection Operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
-
self consistent Projection Operator theory for quantum many body systems
Physical Review B, 2014Co-Authors: Peter Degenfeldschonburg, Michael J HartmannAbstract:We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our Projection Operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides a novel interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of non-equilibrium states in closed and stationary states in driven-dissipative systems.
-
self consistent Projection Operator theory for quantum many body systems
Physical Review B, 2014Co-Authors: Peter Degenfeldschonburg, Michael J HartmannAbstract:We derive an exact equation of motion for the reduced density matrices of individual subsystems of quantum many-body systems of any lattice dimension and arbitrary system size. Our Projection Operator based theory yields a highly efficient analytical and numerical approach. Besides its practical use it provides an interpretation and systematic extension of mean-field approaches and an adaption of open quantum systems theory to settings where a dynamically evolving environment has to be taken into account. We show its high accuracy for two significant classes of complex quantum many-body dynamics, unitary evolutions of nonequilibrium states in closed and stationary states in driven-dissipative systems.
Heinzpeter Breuer - One of the best experts on this subject based on the ideXlab platform.
-
Projection Operator approach to transport in complex single particle quantum systems
arXiv: Statistical Mechanics, 2009Co-Authors: Robin Steinigeweg, Heinzpeter Breuer, Jochen Gemmer, Heinzjurgen SchmidtAbstract:We discuss the time-convolutionless (TCL) Projection Operator approach to transport in closed quantum systems. The Projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. In particular, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems corresponding to quasi one-dimensional structures which consist of identical or similar many-level subunits. Such modular quantum systems are demonstrated to represent many physical situations and several examples of complex single-particle models are analyzed in detail. For these quantum systems lowest order TCL is shown to represent an efficient tool which also allows to investigate the dependence of transport on the considered length scale. To estimate the range of validity of the obtained equations of motion we extend the standard Projection to include additional degrees of freedom which model non-Markovian effects of higher orders.
-
correlated Projection Operator approach to non markovian dynamics in spin baths
Physical Review A, 2007Co-Authors: Jan Fischer, Heinzpeter BreuerAbstract:The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated Projection superOperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated Projection Operator technique significantly improves the standard methods and can be applied to many physical problems such as the hyperfine interaction in a quantum dot.
-
the time convolutionless Projection Operator technique in the quantum theory of dissipation and decoherence
Annals of Physics, 2001Co-Authors: Heinzpeter Breuer, Bernd Kappler, Francesco PetruccioneAbstract:Abstract The time-convolutionless Projection Operator method is used to investigate the non-Markovian dynamics of open quantum systems. On the basis of this method a systematic perturbation expansion for the reduced density matrix equation is obtained involving a time-dependent generator which is local in time. This formalism is generalized to enable the treatment of system-environment correlations in the initial state, which arise in the computation of equilibrium correlation functions or from the preparation of the system by a quantum measurement. The general method is illustrated by means of the damped harmonic oscillator and of the spin-boson model. The perturbation expansion of the equation of motion is applied to a study of relaxation and dephasing processes and to the determination of the stationary state and of equilibrium correlation functions. Special emphasis is laid on the construction of general, computable error estimates which allow the explicit validation of the obtained results. In particular, the parameter regime for which an expansion of the equation of motion to fourth order yields reliable results is determined. The results clearly reveal that a large range of physically relevant parameters, in particular those that might be interesting for experiments on macroscopic quantum coherence phenomena, can already be treated using the expansion to fourth order. It is thus demonstrated that the time-convolutionless Projection Operator technique provides a transparent and technically feasible method to go beyond the Markovian approximation in the study of open quantum systems.
Carlos Navarretebenlloch - One of the best experts on this subject based on the ideXlab platform.
-
self consistent Projection Operator theory in nonlinear quantum optical systems a case study on degenerate optical parametric oscillators
Physical Review A, 2015Co-Authors: Peter Degenfeldschonburg, Carlos Navarretebenlloch, Michael J HartmannAbstract:Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent Projection Operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
-
self consistent Projection Operator theory in nonlinear quantum optical systems a case study on degenerate optical parametric oscillators
Physical Review A, 2015Co-Authors: Peter Degenfeldschonburg, Carlos Navarretebenlloch, Michael J HartmannAbstract:Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. We apply the recently developed self-consistent Projection Operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with a high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.
Wolfgang Domcke - One of the best experts on this subject based on the ideXlab platform.
-
theory of resonance and threshold effects in electron molecule collisions the Projection Operator approach
Physics Reports, 1991Co-Authors: Wolfgang DomckeAbstract:Abstract A review is given of the development of the Projection-Operator formalism of Feshbach towards a comprehensive theory of resonance and threshold effects in electron-molecule collisions. The definition and explicit construction of the appropriate projectors is discussed. The threshold behavior of the singularities of the analytically continued fixed-nuclei electron-molecule scattering matrix is analyzed in order to characterize threshold effects in vibrational excitation by electron impact and dissociative electron attachment. The theory of the dynamics of electron-molecule collision complexes (vibration, dissociation, and autodetachment) is developed, using the methods of time-independent scattering theory as well as a time-dependent wave-packet description. The present stage of development of the theory is illustrated by the review of a few representative applications.
