4,234 research outputs found
Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
We derive relations between various observables for N particles with
zero-range or short-range interactions, in continuous space or on a lattice, in
two or three dimensions, in an arbitrary external potential. Some of our
results generalise known relations between large-momentum behavior of the
momentum distribution, short-distance behavior of the pair correlation function
and of the one-body density matrix, derivative of the energy with respect to
the scattering length or to time, and the norm of the regular part of the
wavefunction; in the case of finite-range interactions, the interaction energy
is also related to dE/da. The expression relating the energy to a functional of
the momentum distribution is also generalised, and is found to break down for
Efimov states with zero-range interactions, due to a subleading oscillating
tail in the momentum distribution. We also obtain new expressions for the
derivative of the energy of a universal state with respect to the effective
range, the derivative of the energy of an efimovian state with respect to the
three-body parameter, and the second order derivative of the energy with
respect to the inverse (or the logarithm in the two-dimensional case) of the
scattering length. The latter is negative at fixed entropy. We use exact
relations to compute corrections to exactly solvable three-body problems and
find agreement with available numerics. For the unitary gas, we compare exact
relations to existing fixed-node Monte-Carlo data, and we test, with existing
Quantum Monte Carlo results on different finite range models, our prediction
that the leading deviation of the critical temperature from its zero range
value is linear in the interaction effective range r_e with a model independent
numerical coefficient.Comment: 51 pages, 5 figures. Split into three articles: Phys. Rev. A 83,
063614 (2011) [arXiv:1103.5157]; Phys. Rev. A 86, 013626 (2012)
[arXiv:1204.3204]; Phys. Rev. A 86, 053633 (2012) [ arXiv:1210.1784
Circular photon drag effect in bulk tellurium
The circular photon drag effect is observed in a bulk semiconductor. The
photocurrent caused by a transfer of both translational and angular momenta of
light to charge carriers is detected in tellurium in the mid-infrared frequency
range. Dependencies of the photocurrent on the light polarization and on the
incidence angle agree with the symmetry analysis of the circular photon drag
effect. Microscopic models of the effect are developed for both intra- and
inter-subband optical absorption in the valence band of tellurium. The shift
contribution to the circular photon drag current is calculated. An observed
decrease of the circular photon drag current with increase of the photon energy
is explained by the theory for inter-subband optical transitions. Theoretical
estimates of the circular photon drag current agree with the experimental data.Comment: 8 pages, 4 figure
Global in Time Solutions to Kolmogorov-Feller Pseudodifferential Equations with Small Parameter
The goal in this paper is to demonstrate a new method for constructing
global-in-time approximate (asymptotic) solutions of (pseudodifferential)
parabolic equations with a small parameter. We show that, in the leading term,
such a solution can be constructed by using characteristics, more precisely, by
using solutions of the corresponding Hamiltonian system and without using any
integral representation. For completeness, we also briefly describe the
well-known scheme developed by V.P.Maslov for constructing global-in-time
solutions.Comment: 27 page
Observation of macroscopic Landau-Zener transitions in a superconducting device
A two-level system traversing a level anticrossing has a small probability to
make a so-called Landau-Zener (LZ) transition between its energy bands, in
deviation from simple adiabatic evolution. This effect takes on renewed
relevance due to the observation of quantum coherence in superconducting qubits
(macroscopic "Schrodinger cat" devices). We report an observation of LZ
transitions in an Al three-junction qubit coupled to a Nb resonant tank
circuit.Comment: REVTeX4, 4pp., 4 EPS figures. v2: clarifications added; final, to
appear in EP
Three-body problem for ultracold atoms in quasi-one-dimensional traps
We study the three-body problem for both fermionic and bosonic cold atom
gases in a parabolic transverse trap of lengthscale . For this
quasi-one-dimensional (1D) problem, there is a two-body bound state (dimer) for
any sign of the 3D scattering length , and a confinement-induced scattering
resonance. The fermionic three-body problem is universal and characterized by
two atom-dimer scattering lengths, and . In the tightly bound
`dimer limit', , we find , and is linked
to the 3D atom-dimer scattering length. In the weakly bound `BCS limit',
, a connection to the Bethe Ansatz is established, which
allows for exact results. The full crossover is obtained numerically. The
bosonic three-body problem, however, is non-universal: and
depend both on and on a parameter related to the sharpness of
the resonance. Scattering solutions are qualitatively similar to fermionic
ones. We predict the existence of a single confinement-induced three-body bound
state (trimer) for bosons.Comment: 20 pages, 6 figures, accepted for publication in PRA, appendix on the
derivation of an integral formula for the Hurvitz zeta functio
Method for direct identification of optimum modal values of dynamical systems
The synthesis method of a dynamic system by successive solutions of two systems of algebraic equations, variables that are characteristic polynomial coefficients and mechanical parameters of the system
Underthreshold resonances in three-particle molecular systems
To determine the lifetimes of Efimov states of negative two-atomic ions, the
problem of resonance scattering of a light particle on a pair of identical
particles has been considered. An analytic expression has been obtained for
resonance widths in the limit of forces of zero radius and low binding energies
in pairs. Calculations are compared with the numerical solution of the Faddeev
integral equations in a wide region of masses of the light particle. It is
shown that the widths of underthreshold resonances in the scattering amplitude
obtained from the integral equations with the Yamaguchi potential are well
described by the analytic expression, which allows this expression to be used
in the mass region inaccessible for numerical calculations. It has been
concluded that the lifetime of highly excited negative molecular ions with a
binding energy close to the threshold of disintegration is practically
unlimited.Comment: Latex, 15 page
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