20,154 research outputs found
Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
Using the parametrically driven harmonic oscillator as a working example, we
study two different Markovian approaches to the quantum dynamics of a
periodically driven system with dissipation. In the simpler approach, the
driving enters the master equation for the reduced density operator only in the
Hamiltonian term. An improved master equation is achieved by treating the
entire driven system within the Floquet formalism and coupling it to the
reservoir as a whole. The different ensuing evolution equations are compared in
various representations, particularly as Fokker-Planck equations for the Wigner
function. On all levels of approximation, these evolution equations retain the
periodicity of the driving, so that their solutions have Floquet form and
represent eigenfunctions of a non-unitary propagator over a single period of
the driving. We discuss asymptotic states in the long-time limit as well as the
conservative and the high-temperature limits. Numerical results obtained within
the different Markov approximations are compared with the exact path-integral
solution. The application of the improved Floquet-Markov scheme becomes
increasingly important when considering stronger driving and lower
temperatures.Comment: 29 pages, 7 figure
Wigner-function formalism applied to semiconductor quantum devices: Need for nonlocal scattering models
In designing and optimizing new-generation nanomaterials and related quantum
devices, dissipation versus decoherence phenomena are often accounted for via
local scattering models, such as relaxation-time and Boltzmann-like schemes.
Here we show that the use of such local scattering approaches within the
Wigner-function formalism may lead to unphysical results, namely anomalous
suppression of intersubband relaxation, incorrect thermalization dynamics, and
violation of probability-density positivity. Furthermore, we propose a
quantum-mechanical generalization of relaxation-time and Boltzmann-like models,
resulting in nonlocal scattering superoperators that enable one to overcome
such limitations.Comment: 12 pages, 7 figure
Phase-space analysis of bosonic spontaneous emission
We present phase-space techniques for the modelling of spontaneous emission
in two-level bosonic atoms. The positive-P representation is shown to give a
full and complete description and can be further developed to give exact
treatments of the interaction of degenerate bosons with the electromagnetic
field in a given experimental situation. The Wigner representation, even when
truncated at second order, is shown to need a doubling of the phase-space to
allow for a positive-definite diffusion matrix in the appropriate Fokker-Planck
equation and still fails to agree with the full quantum results of the
positive-P representation. We show that quantum statistics and correlations
between the ground and excited states affect the dynamics of the emission
process, so that it is in general non-exponential.Comment: 16 pages, 6 figure
Numerical approaches to time evolution of complex quantum systems
We examine several numerical techniques for the calculation of the dynamics
of quantum systems. In particular, we single out an iterative method which is
based on expanding the time evolution operator into a finite series of
Chebyshev polynomials. The Chebyshev approach benefits from two advantages over
the standard time-integration Crank-Nicholson scheme: speedup and efficiency.
Potential competitors are semiclassical methods such as the Wigner-Moyal or
quantum tomographic approaches. We outline the basic concepts of these
techniques and benchmark their performance against the Chebyshev approach by
monitoring the time evolution of a Gaussian wave packet in restricted
one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes
and the motion in anharmonic potentials. Finally we apply the prominent
Chebyshev technique to two highly non-trivial problems of current interest: (i)
the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the
spatiotemporal evolution of polaron states in finite quantum systems. Here,
depending on the disorder/electron-phonon coupling strength and the device
dimensions, we observe transmission or localisation of the matter wave.Comment: 8 pages, 3 figure
Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
We review phase space techniques based on the Wigner representation that
provide an approximate description of dilute ultra-cold Bose gases. In this
approach the quantum field evolution can be represented using equations of
motion of a similar form to the Gross-Pitaevskii equation but with stochastic
modifications that include quantum effects in a controlled degree of
approximation. These techniques provide a practical quantitative description of
both equilibrium and dynamical properties of Bose gas systems. We develop
versions of the formalism appropriate at zero temperature, where quantum
fluctuations can be important, and at finite temperature where thermal
fluctuations dominate. The numerical techniques necessary for implementing the
formalism are discussed in detail, together with methods for extracting
observables of interest. Numerous applications to a wide range of phenomena are
presented.Comment: 110 pages, 32 figures. Updated to address referee comments. To appear
in Advances in Physic
Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots
We provide a quantitative determination of the crystallization onset for two
electrons in a parabolic two-dimensional confinement. This system is shown to
be well described by a roto-vibrational model, Wigner crystallization occurring
when the rotational motion gets decoupled from the vibrational one. The Wigner
molecule thus formed is characterized by its moment of inertia and by the
corresponding sequence of rotational excited states. The role of a vertical
magnetic field is also considered. Additional support to the analysis is given
by the Hartree-Fock phase diagram for the ground state and by the random-phase
approximation for the moment of inertia and vibron excitations.Comment: 10 pages, 8 figures, replaced by the published versio
Localization and Pattern Formation in Quantum Physics. I. Phenomena of Localization
In these two related parts we present a set of methods, analytical and
numerical, which can illuminate the behaviour of quantum system, especially in
the complex systems. The key points demonstrating advantages of this approach
are: (i) effects of localization of possible quantum states, more proper than
"gaussian-like states"; (ii) effects of non-perturbative multiscales which
cannot be calculated by means of perturbation approaches; (iii) effects of
formation of complex quantum patterns from localized modes or classification
and possible control of the full zoo of quantum states, including (meta) stable
localized patterns (waveletons). We'll consider calculations of Wigner
functions as the solution of Wigner-Moyal-von Neumann equation(s) corresponding
to polynomial Hamiltonians. Modeling demonstrates the appearance of (meta)
stable patterns generated by high-localized (coherent) structures or
entangled/chaotic behaviour. We can control the type of behaviour on the level
of reduced algebraical variational system. At the end we presented the
qualitative definition of the Quantum Objects in comparison with their
Classical Counterparts, which natural domain of definition is the category of
multiscale/multiresolution decompositions according to the action of
internal/hidden symmetry of the proper realization of scales of functional
spaces. It gives rational natural explanation of such pure quantum effects as
``self-interaction''(self-interference) and instantaneous quantum interaction.Comment: LaTeX2e, spie.cls, 13 pages, 15 figures, submitted to Proc. of SPIE
Meeting, The Nature of Light: What is a Photon? Optics & Photonics, SP200,
San Diego, CA, July-August, 200
Non-adiabacity and large flucutations in a many particle Landau Zener problem
We consider the behavior of an interacting many particle system under slow
external driving -- a many body generalization of the Landau-Zener paradigm. We
find that a conspiracy of interactions and driving leads to physics profoundly
different from that of the single particle limit: for practically all values of
the driving rate the particle distributions in Hilbert space are very broad, a
phenomenon caused by a strong amplification of quantum fluctuations in the
driving process. These fluctuations are 'non-adiabatic' in that even at very
slow driving it is exceedingly difficult to push the center of the distribution
towards the limit of full ground state occupancy. We obtain these results by a
number of complementary theoretical approaches, including diagrammatic
perturbation theory, semiclassical analysis, and exact diagonalization.Comment: 25 pages, 16 figure
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