485 research outputs found
The thermal conductivity reduction in HgTe/CdTe superlattices
The techniques used previously to calculate the three-fold thermal
conductivity reduction due to phonon dispersion in GaAs/AlAs superlattices
(SLs) are applied to HgTe/CdTe SLs. The reduction factor is approximately the
same, indicating that this SL may be applicable both as a photodetector and a
thermoelectric cooler.Comment: 5 pages, 2 figures; to be published in Journal of Applied Physic
Phonon Dispersion Effects and the Thermal Conductivity Reduction in GaAs/AlAs Superlattices
The experimentally observed order-of-magnitude reduction in the thermal
conductivity along the growth axis of (GaAs)_n/(AlAs)_n (or n x n)
superlattices is investigated theoretically for (2x2), (3x3) and (6x6)
structures using an accurate model of the lattice dynamics. The modification of
the phonon dispersion relation due to the superlattice geometry leads to
flattening of the phonon branches and hence to lower phonon velocities. This
effect is shown to account for a factor-of-three reduction in the thermal
conductivity with respect to bulk GaAs along the growth direction; the
remainder is attributable to a reduction in the phonon lifetime. The
dispersion-related reduction is relatively insensitive to temperature (100 < T
< 300K) and n. The phonon lifetime reduction is largest for the (2x2)
structures and consistent with greater interface scattering. The thermal
conductivity reduction is shown to be appreciably more sensitive to GaAs/AlAs
force constant differences than to those associated with molecular masses.Comment: 5 figure
Statistical Properties of Many Particle Eigenfunctions
Wavefunction correlations and density matrices for few or many particles are
derived from the properties of semiclassical energy Green functions. Universal
features of fixed energy (microcanonical) random wavefunction correlation
functions appear which reflect the emergence of the canonical ensemble as the
number of particles approaches infinity. This arises through a little known
asymptotic limit of Bessel functions. Constraints due to symmetries,
boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure
Eigenstate Structure in Graphs and Disordered Lattices
We study wave function structure for quantum graphs in the chaotic and
disordered regime, using measures such as the wave function intensity
distribution and the inverse participation ratio. The result is much less
ergodicity than expected from random matrix theory, even though the spectral
statistics are in agreement with random matrix predictions. Instead, analytical
calculations based on short-time semiclassical behavior correctly describe the
eigenstate structure.Comment: 4 pages, including 2 figure
Semiclassical Construction of Random Wave Functions for Confined Systems
We develop a statistical description of chaotic wavefunctions in closed
systems obeying arbitrary boundary conditions by combining a semiclassical
expression for the spatial two-point correlation function with a treatment of
eigenfunctions as Gaussian random fields. Thereby we generalize Berry's
isotropic random wave model by incorporating confinement effects through
classical paths reflected at the boundaries. Our approach allows to explicitly
calculate highly non-trivial statistics, such as intensity distributions, in
terms of usually few short orbits, depending on the energy window considered.
We compare with numerical quantum results for the Africa billiard and derive
non-isotropic random wave models for other prominent confinement geometries.Comment: To be submitted to Physical Review Letter
Avoided intersections of nodal lines
We consider real eigen-functions of the Schr\"odinger operator in 2-d. The
nodal lines of separable systems form a regular grid, and the number of nodal
crossings equals the number of nodal domains. In contrast, for wave functions
of non integrable systems nodal intersections are rare, and for random waves,
the expected number of intersections in any finite area vanishes. However,
nodal lines display characteristic avoided crossings which we study in the
present work. We define a measure for the avoidance range and compute its
distribution for the random waves ensemble. We show that the avoidance range
distribution of wave functions of chaotic systems follow the expected random
wave distributions, whereas for wave functions of classically integrable but
quantum non-separable wave functions, the distribution is quite different.
Thus, the study of the avoidance distribution provides more support to the
conjecture that nodal structures of chaotic systems are reproduced by the
predictions of the random waves ensemble.Comment: 12 pages, 4 figure
Localization of Eigenfunctions in the Stadium Billiard
We present a systematic survey of scarring and symmetry effects in the
stadium billiard. The localization of individual eigenfunctions in Husimi phase
space is studied first, and it is demonstrated that on average there is more
localization than can be accounted for on the basis of random-matrix theory,
even after removal of bouncing-ball states and visible scars. A major point of
the paper is that symmetry considerations, including parity and time-reversal
symmetries, enter to influence the total amount of localization. The properties
of the local density of states spectrum are also investigated, as a function of
phase space location. Aside from the bouncing-ball region of phase space,
excess localization of the spectrum is found on short periodic orbits and along
certain symmetry-related lines; the origin of all these sources of localization
is discussed quantitatively and comparison is made with analytical predictions.
Scarring is observed to be present in all the energy ranges considered. In
light of these results the excess localization in individual eigenstates is
interpreted as being primarily due to symmetry effects; another source of
excess localization, scarring by multiple unstable periodic orbits, is smaller
by a factor of .Comment: 31 pages, including 10 figure
Regularization of Tunneling Rates with Quantum Chaos
We study tunneling in various shaped, closed, two-dimensional, flat
potential, double wells by calculating the energy splitting between symmetric
and anti-symmetric state pairs. For shapes that have regular or nearly regular
classical behavior (e.g. rectangular or circular) the tunneling rates vary
greatly over wide ranges often by several orders of magnitude. However, for
well shapes that admit more classically chaotic behavior (e.g. the stadium, the
Sinai billiard) the range of tunneling rates narrows, often by orders of
magnitude. This dramatic narrowing appears to come from destabilization of
periodic orbits in the regular wells that produce the largest and smallest
tunneling rates and causes the splitting vs. energy relation to take on a
possibly universal shape. It is in this sense that we say the quantum chaos
regularizes the tunneling rates
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