1,538 research outputs found
Quantization of generic chaotic 3D billiard with smooth boundary II: structure of high-lying eigenstates
This is the first survey of highly excited eigenstates of a chaotic 3D
billiard. We introduce a strongly chaotic 3D billiard with a smooth boundary
and we manage to calculate accurate eigenstates with sequential number (of a
48-fold desymmetrized billiard) about 45,000. Besides the brute-force
calculation of 3D wavefunctions we propose and illustrate another two
representations of eigenstates of quantum 3D billiards: (i) normal derivative
of a wavefunction over the boundary surface, and (ii) ray - angular momentum
representation. The majority of eigenstates is found to be more or less
uniformly extended over the entire energy surface, as expected, but there is
also a fraction of strongly localized - scarred eigenstates which are localized
either (i) on to classical periodic orbits or (ii) on to planes which carry
(2+2)-dim classically invariant manifolds, although the classical dynamics is
strongly chaotic and non-diffusive.Comment: 12 pages in plain Latex (5 figures in PCL format available upon
request) Submitted to Phys.Lett.
Quantum invariants of motion in a generic many-body system
Dynamical Lie-algebraic method for the construction of local quantum
invariants of motion in non-integrable many-body systems is proposed and
applied to a simple but generic toy model, namely an infinite kicked
chain of spinless fermions. Transition from integrable via {pseudo-integrable
(\em intermediate}) to quantum ergodic (quantum mixing) regime in parameter
space is investigated. Dynamical phase transition between ergodic and
intermediate (neither ergodic nor completely integrable) regime in
thermodynamic limit is proposed. Existence or non-existence of local
conservation laws corresponds to intermediate or ergodic regime, respectively.
The computation of time-correlation functions of typical observables by means
of local conservation laws is found fully consistent with direct calculations
on finite systems.Comment: 4 pages in REVTeX with 5 eps figures include
Quantization of generic chaotic 3D billiard with smooth boundary I: energy level statistic
Numerical calculation and analysis of extremely high-lying energy spectra,
containing thousands of levels with sequential quantum number up to 62,000 per
symmetry class, of a generic chaotic 3D quantum billiard is reported. The shape
of the billiard is given by a simple and smooth de formation of a unit sphere
which gives rise to (almost) fully chaotic classical dynamics. We present an
analysis of (i) quantum length spectrum whose smooth part agrees with the 3D
Weyl formula and whose oscillatory part is peaked around the periods of
classical periodic orbits, (ii) nearest neighbor level spacing distribution and
(iii) number variance.
Although the chaotic classical dynamics quickly and uniformly explores almost
entire energy shell, while the measure of the regular part of phase space is
insignificantly small, we find small but significant deviations from GOE
statistics which are explained in terms of localization of eigenfunctions onto
lower dimensional classically invariant manifolds.Comment: 10 pages in plain Latex (6 figures in PCL format available upon
request) submitted to Phys. Lett.
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
Explicit solution for the 2-point correlation function in a non-equilibrium
steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in
the Lindblad formulation is provided. A non-equilibrium quantum phase
transition from exponentially decaying correlations to long-range order is
discussed analytically. In the regime of long-range order a new phenomenon of
correlation resonances is reported, where the correlation response of the
system is unusually high for certain discrete values of the external bulk
parameter, e.g. the magnetic field.Comment: 20 Pages, 5 figure
Exact time-correlation functions of quantum Ising chain in a kicking transversal magnetic field
Spectral analysis of the {\em adjoint} propagator in a suitable Hilbert space
(and Lie algebra) of quantum observables in Heisenberg picture is discussed as
an alternative approach to characterize infinite temperature dynamics of
non-linear quantum many-body systems or quantum fields, and to provide a bridge
between ergodic properties of such systems and the results of classical ergodic
theory. We begin by reviewing some recent analytic and numerical results along
this lines. In some cases the Heisenberg dynamics inside the subalgebra of the
relevant quantum observables can be mapped explicitly into the (conceptually
much simpler) Schr\" odinger dynamics of a single one-(or few)-dimensional
quantum particle. The main body of the paper is concerned with an application
of the proposed method in order to work out explicitly the general spectral
measures and the time correlation functions in {\em a quantum Ising spin 1/2
chain in a periodically kicking transversal magnetic field}, including the
results for the simpler autonomous case of a static magnetic field in the
appropriate limit. The main result, being a consequence of a purely continuous
non-trivial part of the spectrum, is that the general time-correlation
functions decay to their saturation values as .Comment: 12 pages with 4 eps-figure
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