1,391 research outputs found
Quantum ergodicity for Pauli Hamiltonians with spin 1/2
Quantum ergodicity, which expresses the semiclassical convergence of almost
all expectation values of observables in eigenstates of the quantum Hamiltonian
to the corresponding classical microcanonical average, is proven for
non-relativistic quantum particles with spin 1/2. It is shown that quantum
ergodicity holds, if a suitable combination of the classical translational
dynamics and the spin dynamics along the trajectories of the translational
motion is ergodic.Comment: 20 pages, no figure
Superconducting transition temperatures and coherence length in non s-wave pairing materials correlated with spin-fluctuation mediated interaction
Following earlier work on electron or hole liquids flowing through assemblies
with magnetic fluctuations, we have recently exposed a marked correlation of
the superconducting temperature Tc, for non s-wave pairing materials, with
coherence length xi and effective mass m*. The very recent study of Abanov et
al. [Europhys. Lett. 54, 488 (2001)] and the prior investigation of Monthoux
and Lonzarich [Phys. Rev. B 59, 14598 (1999)] have each focussed on the concept
of a spin-fluctuation temperature T_sf, which again is intimately related to
Tc. For the d-wave pairing via antiferromagnetic spin fluctuations in the
cuprates, these studies are brought into close contact with our own work, and
the result is that k_B T_sf ~ hbar^2 / m* xi^2. This demonstrates that xi is
also determined by such antiferromagnetic spin-fluctuation mediated pair
interaction. The coherence length in units of the lattice spacing is then
essentially given in the cuprates as the square root of the ratio of two
characteristic energies, namely: the kinetic energy of localization of a charge
carrier of mass m* in a specified magnetic correlation length to the hopping
energy. The quasi-2D ruthenate Sr_2RuO_4, with Tc ~ 1.3 K, has p-wave
spin-triplet pairing and so is also briefly discussed here.Comment: Accepted for publication in Phys. Rev.
Quantum and Topological Criticalities of Lifshitz Transition in Two-Dimensional Correlated Electron Systems
We study electron correlation effects on quantum criticalities of Lifshitz
transitions at zero temperature, using the mean-field theory based on a
preexisting symmetry-broken order, in two-dimensional systems. In the presence
of interactions, Lifshitz transitions may become discontinuous in contrast to
the continuous transition in the original proposal by Lifshitz for
noninteracting systems. We focus on the quantum criticality at the endpoint of
discontinuous Lifshitz transitions, which we call the marginal quantum critical
point. It shows remarkable criticalities arising from its nature as a
topological transition. At the point, for the canonical ensemble, the
susceptibility of the order parameter chi is found to diverge as ln 1/|delta
Delta| when the ``neck'' of the Fermi surface collapses at the van Hove
singularity. More remarkably, it diverges as 1/|delta Delta| when the
electron/hole pocket of the Fermi surface vanishes. Here delta Delta is the
amplitude of the mean field measured from the Lifshitz critical point. On the
other hand, for the grand canonical ensemble, the discontinuous transitions
appear as the electronic phase separation and the endpoint of the phase
separation is the marginal quantum critical point. Especially, when a pocket of
the Fermi surface vanishes, the uniform charge compressibility kappa diverges
as 1/|delta n|, instead of chi, where delta n is the electron density measured
from the critical point. Accordingly, Lifshitz transition induces large
fluctuations represented by diverging chi and/or kappa. Such fluctuations must
be involved in physics of competing orders and influence diversity of strong
correlation effects.Comment: 16 pages, 15 figures, to appear in Jounal of the Physical Society of
Japa
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
We review the latest progress and properties of the families of bright and
dark one-dimensional periodic waves propagating in saturable Kerr-type and
quadratic nonlinear media. We show how saturation of the nonlinear response
results in appearance of stability (instability) bands in focusing (defocusing)
medium, which is in sharp contrast with the properties of periodic waves in
Kerr media. One of the key results discovered is the stabilization of
multicolor periodic waves in quadratic media. In particular, dark-type waves
are shown to be metastable, while bright-type waves are completely stable in a
broad range of energy flows and material parameters. This yields the first
known example of completely stable periodic wave patterns propagating in
conservative uniform media supporting bright solitons. Such results open the
way to the experimental observation of the corresponding self-sustained
periodic wave patterns.Comment: 29 pages, 10 figure
Finsler geometry modeling of reverse piezoelectric effect in PVDF
We apply the Finsler geometry (FG) modeling technique to study the electric field-induced strain in ferroelectric polymers. Polyvinylidene difluoride (PVDF) has a negative longitudinal piezoelectric coefficient, which is unusual in ferroelectrics, and therefore the shape changes in this material are hard to predict. We find that the results of Monte Carlo simulations for the FG model are in good agreement with experimental strain-electric field curves of PVDF-based polymers in both longitudinal and transverse directions. This implies that FG modeling is suitable for reproducing the reverse piezoelectric effect in PVDF
Zitterbewegung and semiclassical observables for the Dirac equation
In a semiclassical context we investigate the Zitterbewegung of relativistic
particles with spin 1/2 moving in external fields. It is shown that the
analogue of Zitterbewegung for general observables can be removed to arbitrary
order in \hbar by projecting to dynamically almost invariant subspaces of the
quantum mechanical Hilbert space which are associated with particles and
anti-particles. This not only allows to identify observables with a
semiclassical meaning, but also to recover combined classical dynamics for the
translational and spin degrees of freedom. Finally, we discuss properties of
eigenspinors of a Dirac-Hamiltonian when these are projected to the almost
invariant subspaces, including the phenomenon of quantum ergodicity
Resonant nonstationary amplification of polychromatic laser pulses and conical emission in an optically dense ensemble of neon metastable atoms
Experimental and numerical investigation of single-beam and pump-probe
interaction with a resonantly absorbing dense extended medium under strong and
weak field-matter coupling is presented. Significant probe beam amplification
and conical emission were observed. Under relatively weak pumping and high
medium density, when the condition of strong coupling between field and
resonant matter is fulfilled, the probe amplification spectrum has a form of
spectral doublet. Stronger pumping leads to the appearance of a single peak of
the probe beam amplification at the transition frequency. The greater probe
intensity results in an asymmetrical transmission spectrum with amplification
at the blue wing of the absorption line and attenuation at the red one. Under
high medium density, a broad band of amplification appears. Theoretical model
is based on the solution of the Maxwell-Bloch equations for a two-level system.
Different types of probe transmission spectra obtained are attributed to
complex dynamics of a coherent medium response to broadband polychromatic
radiation of a multimode dye laser.Comment: 9 pages, 13 figures, corrected, Fig.8 was changed, to be published in
Phys. Rev.
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