394 research outputs found
On non-coercive mixed problems for parameter-dependent elliptic operators
We consider a (generally, non-coercive) mixed boundary value problem in a
bounded domain of for a second order parameter-dependent
elliptic differential operator with complex-valued
essentially bounded measured coefficients and complex parameter . The
differential operator is assumed to be of divergent form in , the boundary
operator is of Robin type with possible pseudo-differential
components on . The boundary of is assumed to be a Lipschitz
surface. Under these assumptions the pair induces
a holomorphic family of Fredholm operators in
suitable Hilbert spaces , of Sobolev type. If the argument
of the complex-valued multiplier of the parame\-ter in is continuous and the coefficients related to second order
derivatives of the operator are smooth then we prove that the operators
are conti\-nu\-ously invertible for all with
sufficiently large modulus on each ray on the complex plane
where the differential operator is
parameter-dependent elliptic. We also describe reasonable conditions for the
system of root functions related to the family to be (doubly)
complete in the spaces , and the Lebesgue space
Unconventional fermionic pairing states in a monochromatically tilted optical lattice
We study the one-dimensional attractive fermionic Hubbard model under the influence of periodic driving with
the time-dependent density matrix renormalization group method. We show that the system can be driven into
an unconventional pairing state characterized by a condensate made of Cooper pairs with a finite center-of-mass
momentum similar to a Fulde-Ferrell state. We obtain results both in the laboratory and the rotating reference
frames demonstrating that the momentum of the condensate can be finely tuned by changing the ratio between
the amplitude and the frequency of the driving. In particular, by quenching this ratio to the value corresponding to
suppression of the tunneling and the Coulomb interaction strength to zero, we are able to “freeze” the condensate.
We finally study the effects of different initial conditions and compare our numerical results to those obtained from
a time-independent Floquet theory in the large frequency regime. Our work offers the possibility of engineering
and controlling unconventional pairing states in fermionic condensates.This work was conducted at the Center for Nanophase Materials Sciences, sponsored by the Scientific User Facilities Division (SUFD), Basic Energy Sciences (BES), U.S. Department of Energy (DOE), under contract with UT-Battelle. A.N. acknowledges support by the Center for Nanophase Materials Sciences and by the Early Career Research program, SUFD, BES, DOE. A.E.F. acknowledges the DOE, Office of Basic Energy Sciences, for support under Grant No. DE-SC0014407. A.P. was supported by NSF DMR-1506340, ARO W911NF1410540, and AFOSR FA9550-16-1-0334. (Scientific User Facilities Division (SUFD); Basic Energy Sciences (BES); U.S. Department of Energy (DOE); UT-Battelle; Center for Nanophase Materials Sciences; Early Career Research program; SUFD; BES; DOE; DE-SC0014407 - DOE, Office of Basic Energy Sciences; NSF DMR-1506340; ARO W911NF1410540; AFOSR FA9550-16-1-0334)Published versio
Breakdown of the adiabatic limit in low dimensional gapless systems
It is generally believed that a generic system can be reversibly transformed
from one state into another by sufficiently slow change of parameters. A
standard argument favoring this assertion is based on a possibility to expand
the energy or the entropy of the system into the Taylor series in the ramp
speed. Here we show that this argumentation is only valid in high enough
dimensions and can break down in low-dimensional gapless systems. We identify
three generic regimes of a system response to a slow ramp: (A) mean-field, (B)
non-analytic, and (C) non-adiabatic. In the last regime the limits of the ramp
speed going to zero and the system size going to infinity do not commute and
the adiabatic process does not exist in the thermodynamic limit. We support our
results by numerical simulations. Our findings can be relevant to
condensed-matter, atomic physics, quantum computing, quantum optics, cosmology
and others.Comment: 11 pages, 5 figures, to appear in Nature Physics (originally
submitted version
Non-equilibrium coherence dynamics of a soft boson lattice
We study the non-equilibrium evolution of the phase coherence of a
Bose-Einstein condensate (BEC) in a one dimensional optical lattice, as the
lattice is suddenly quenched from an insulating to a superfluid state. We
observe slowly damped phase coherence oscillations in the regime of large
filling factor (~100 bosons per site) at a frequency proportional to the
generalized Josephson frequency. The truncated Wigner approximation (TWA)
predicts the frequency of the observed oscillations.Comment: 10 pages. 4 figure
Dynamical Quantum Hall Effect in the Parameter Space
Geometric phases in quantum mechanics play an extraordinary role in
broadening our understanding of fundamental significance of geometry in nature.
One of the best known examples is the Berry phase (M.V. Berry (1984), Proc.
Royal. Soc. London A, 392:45) which naturally emerges in quantum adiabatic
evolution. So far the applicability and measurements of the Berry phase were
mostly limited to systems of weakly interacting quasi-particles, where
interference experiments are feasible. Here we show how one can go beyond this
limitation and observe the Berry curvature and hence the Berry phase in generic
systems as a non-adiabatic response of physical observables to the rate of
change of an external parameter. These results can be interpreted as a
dynamical quantum Hall effect in a parameter space. The conventional quantum
Hall effect is a particular example of the general relation if one views the
electric field as a rate of change of the vector potential. We illustrate our
findings by analyzing the response of interacting spin chains to a rotating
magnetic field. We observe the quantization of this response, which term the
rotational quantum Hall effect.Comment: 7 pages, 5 figures added figure with anisotropic chai
Decay of super-currents in condensates in optical lattices
In this paper we discuss decay of superfluid currents in boson lattice
systems due to quantum tunneling and thermal activation mechanisms. We derive
asymptotic expressions for the decay rate near the critical current in two
regimes, deep in the superfluid phase and close to the superfluid-Mott
insulator transition. The broadening of the transition at the critical current
due to these decay mechanisms is more pronounced at lower dimensions. We also
find that the crossover temperature below which quantum decay dominates is
experimentally accessible in most cases. Finally, we discuss the dynamics of
the current decay and point out the difference between low and high currents.Comment: Contribution to the special issue of Journal of Superconductivity in
honor of Michael Tinkham's 75th birthda
Failure of Scattering Interference in the Pseudogap State of Cuprate Superconductors
We calculate scattering interference patterns for various electronic states
proposed for the pseudogap regime of the cuprate superconductors. The
scattering interference models all produce patterns whose wavelength changes as
a function of energy, in contradiction to the energy-independent wavelength
seen by scanning tunneling microscopy (STM) experiments in the pseudogap state.
This suggests that the patterns seen in STM local density of states
measurements are not due to scattering interference, but are rather the result
of some form of ordering.Comment: To be submitted to Phys. Rev.
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