10,435 research outputs found
Measuring nonadiabaticity of molecular quantum dynamics with quantum fidelity and with its efficient semiclassical approximation
We propose to measure nonadiabaticity of molecular quantum dynamics
rigorously with the quantum fidelity between the Born-Oppenheimer and fully
nonadiabatic dynamics. It is shown that this measure of nonadiabaticity applies
in situations where other criteria, such as the energy gap criterion or the
extent of population transfer, fail. We further propose to estimate this
quantum fidelity efficiently with a generalization of the dephasing
representation to multiple surfaces. Two variants of the multiple-surface
dephasing representation (MSDR) are introduced, in which the nuclei are
propagated either with the fewest-switches surface hopping (FSSH) or with the
locally mean field dynamics (LMFD). The LMFD can be interpreted as the
Ehrenfest dynamics of an ensemble of nuclear trajectories, and has been used
previously in the nonadiabatic semiclassical initial value representation. In
addition to propagating an ensemble of classical trajectories, the MSDR
requires evaluating nonadiabatic couplings and solving the Schr\"{o}dinger (or
more generally, the quantum Liouville-von Neumann) equation for a single
discrete degree of freedom. The MSDR can be also used to measure the importance
of other terms present in the molecular Hamiltonian, such as diabatic
couplings, spin-orbit couplings, or couplings to external fields, and to
evaluate the accuracy of quantum dynamics with an approximate nonadiabatic
Hamiltonian. The method is tested on three model problems introduced by Tully,
on a two-surface model of dissociation of NaI, and a three-surface model
including spin-orbit interactions. An example is presented that demonstrates
the importance of often-neglected second-order nonadiabatic couplings.Comment: 14 pages, 4 figures, submitted to J. Chem. Phy
Steady-state composition of a two-component gas bubble growing in a liquid solution: self-similar approach
The paper presents an analytical description of the growth of a two-component
bubble in a binary liquid-gas solution. We obtain asymptotic self-similar time
dependence of the bubble radius and analytical expressions for the non-steady
profiles of dissolved gases around the bubble. We show that the necessary
condition for the self-similar regime of bubble growth is the constant,
steady-state composition of the bubble. The equation for the steady-state
composition is obtained. We reveal the dependence of the steady-state
composition on the solubility laws of the bubble components. Besides, the
universal, independent from the solubility laws, expressions for the
steady-state composition are obtained for the case of strong supersaturations,
which are typical for the homogeneous nucleation of a bubble.Comment: 12 pages, 2 figure
Entanglement Entropy and Mutual Information Production Rates in Acoustic Black Holes
A method to investigate acoustic Hawking radiation is proposed, where
entanglement entropy and mutual information are measured from the fluctuations
of the number of particles. The rate of entropy radiated per one-dimensional
(1D) channel is given by , where is the sound
acceleration on the sonic horizon. This entropy production is accompanied by a
corresponding formation of mutual information to ensure the overall
conservation of information. The predictions are confirmed using an \emph{ab
initio} analytical approach in transonic flows of 1D degenerate ideal Fermi
fluids.Comment: 4 pages, 1 figure. Supplemental Material (pdf) included in the source
of this manuscrip
Floquet analysis of the modulated two-mode Bose-Hubbard model
We study the tunneling dynamics in a time-periodically modulated two-mode
Bose-Hubbard model using Floquet theory. We consider situations where the
system is in the self-trapping regime and either the tunneling amplitude, the
interaction strength, or the energy difference between the modes is modulated.
In the former two cases, the tunneling is enhanced in a wide range of
modulation frequencies, while in the latter case the resonance is narrow. We
explain this difference with the help of Floquet analysis. If the modulation
amplitude is weak, the locations of the resonances can be found using the
spectrum of the non-modulated Hamiltonian. Furthermore, we use Floquet analysis
to explain the coherent destruction of tunneling (CDT) occurring in a
large-amplitude modulated system. Finally, we present two ways to create a NOON
state (a superposition of particles in mode 1 with zero particles in mode 2
and vice versa). One is based on a coherent oscillation caused by detuning from
a partial CDT. The other makes use of an adiabatic variation of the modulation
frequency. This results in a Landau-Zener type of transition between the ground
state and a NOON-like state.Comment: 16 pages, 11 figures; published in Phys. Rev.
Nuclear State Preparation via Landau-Zener-Stueckelberg transitions in Double Quantum Dots
We theoretically model a nuclear-state preparation scheme that increases the
coherence time of a two-spin qubit in a double quantum dot. The two-electron
system is tuned repeatedly across a singlet-triplet level-anticrossing with
alternating slow and rapid sweeps of an external bias voltage. Using a
Landau-Zener-Stueckelberg model, we find that in addition to a small nuclear
polarization that weakly affects the electron spin coherence, the slow sweeps
are only partially adiabatic and lead to a weak nuclear spin measurement and a
nuclear-state narrowing which prolongs the electron spin coherence. This
resolves some open problems brought up by a recent experiment [D. J. Reilly et
al., Science 321, 817 (2008).]. Based on our description of the weak
measurement, we simulate a system with up to n=200 nuclear spins per dot.
Scaling in n indicates a stronger effect for larger n.Comment: 4.1 pages, 2 figure
Zero Lattice Sound
We study the N_f-flavor Gross-Neveu model in 2+1 dimensions with a baryon
chemical potential mu, using both analytical and numerical methods. In
particular, we study the self-consistent Boltzmann equation in the Fermi liquid
framework using the quasiparticle interaction calculated to O(1/N_f), and find
solutions for zero sound propagation for almost all mu > mu_c, the critical
chemical potential for chiral symmetry restoration. Next we present results of
a numerical lattice simulation, examining temporal correlation functions of
mesons defined using a point-split interpolating operator, and finding evidence
for phonon-like behaviour characterised by a linear dispersion relation in the
long wavelength limit. We argue that our results provide the first evidence for
a collective excitation in a lattice simulation.Comment: 18 pages, 6 figure
A General Information Theoretical Proof for the Second Law of Thermodynamics
We show that the conservation and the non-additivity of the information,
together with the additivity of the entropy make the entropy increase in an
isolated system. The collapse of the entangled quantum state offers an example
of the information non-additivity. Nevertheless, the later is also true in
other fields, in which the interaction information is important. Examples are
classical statistical mechanics, social statistics and financial processes. The
second law of thermodynamics is thus proven in its most general form. It is
exactly true, not only in quantum and classical physics but also in other
processes, in which the information is conservative and non-additive.Comment: 4 page
Magneto-elastic waves in crystals of magnetic molecules
We study magneto-elastic effects in crystals of magnetic molecules. Coupled
equations of motion for spins and sound are derived and the possibility of
strong resonant magneto-acoustic coupling is demonstrated. Dispersion laws for
interacting linear sound and spin excitations are obtained for bulk and surface
acoustic waves. We show that ultrasound can generate inverse population of spin
levels. Alternatively, the decay of the inverse population of spin levels can
generate ultrasound. Possibility of solitary waves of the magnetization
accompanied by the elastic twists is demonstrated.Comment: 8 PR pages, 3 figure
On the conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonances
We explain why the experimental efficiency observed in the conversion of
ultracold Fermi gases of K and Li atoms into diatomic Bose gases
is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow
to pass adiabatically through the Landau Zener transition but faster than ``the
collision rate'' in the gas, and increases beyond 0.5 when it is slower. The
0.5 efficiency limit is due to the preparation of a statistical mixture of two
spin-states, required to enable s-wave scattering. By constructing the
many-body state of the system we show that this preparation yields a mixture of
even and odd parity pair-states, where only even parity can produce molecules.
The odd parity spin-symmetric states must decorrelate before the constituent
atoms can further Feshbach scatter thereby increasing the conversion
efficiency; ``the collision rate'' is the pair decorrelation rate.Comment: 4 pages, 3 figures, final version accepted to Phys. Rev. Let
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