2,309 research outputs found
Observing trajectories with weak measurements in quantum systems in the semiclassical regime
We propose a scheme allowing to observe the evolution of a quantum system in
the semiclassical regime along the paths generated by the propagator. The
scheme relies on performing consecutive weak measurements of the position. We
show how weak trajectories" can be extracted from the pointers of a series of
measurement devices having weakly interacted with the system. The properties of
these "weak trajectories" are investigated and illustrated in the case of a
time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will
appear as Suppl. Material). To be published in Phys Rev Let
Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential
We present an analytical calculation of periodic orbits in the homogeneous
quartic oscillator potential. Exploiting the properties of the periodic
Lam{\'e} functions that describe the orbits bifurcated from the fundamental
linear orbit in the vicinity of the bifurcation points, we use perturbation
theory to obtain their evolution away from the bifurcation points. As an
application, we derive an analytical semiclassical trace formula for the
density of states in the separable case, using a uniform approximation for the
pitchfork bifurcations occurring there, which allows for full semiclassical
quantization. For the non-integrable situations, we show that the uniform
contribution of the bifurcating period-one orbits to the coarse-grained density
of states competes with that of the shortest isolated orbits, but decreases
with increasing chaoticity parameter .Comment: 15 pages, LaTeX, 7 figures; revised and extended version, to appear
in J. Phys. A final version 3; error in eq. (33) corrected and note added in
prin
Thermodynamics of a Trapped Unitary Fermi Gas
We present the first model-independent comparison of recent measurements of
the entropy and of the critical temperature of a unitary Fermi gas, performed
by Luo et al., with the most complete results currently available from finite
temperature Monte Carlo calculations. The measurement of the critical
temperature in a cold fermionic atomic cloud is consistent with a value
in the bulk, as predicted by the present authors in
their Monte Carlo calculations.Comment: 5 pages, 4 figures, published versio
Anomalous Fisher-like zeros for the canonical partition function of noninteracting fermions
Noninteracting fermions, placed in a system with a continuous density of
states, may have zeros in the -fermion canonical partition function on the
positive real axis (or very close to it), even for a small number of
particles. This results in a singular free energy, and instability in other
thermal properties of the system. In the context of trapped fermions in a
harmonic oscillator, these zeros are shown to be unphysical. By contrast,
similar bosonic calculations with continuous density of states yield sensible
results.Noninteracting fermions, placed in a system with a continuous density
of states yield sensible results.Comment: 5 pages and 5 figure
Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems
We investigate cascades of isochronous pitchfork bifurcations of
straight-line librating orbits in some two-dimensional Hamiltonian systems with
mixed phase space. We show that the new bifurcated orbits, which are
responsible for the onset of chaos, are given analytically by the periodic
solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians
with C_ symmetry, they occur alternatingly as Lam\'e functions of period
2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function
appearing in the Lam\'e equation. We also show that the two pairs of orbits
created at period-doubling bifurcations of touch-and-go type are given by two
different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper,
accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of
bifurcations "touch-and-go" replaced by "island-chain
Semiclassical description of shell effects in finite fermion systems
A short survey of the semiclassical periodic orbit theory, initiated by M.
Gutzwiller and generalized by many other authors, is given. Via so-called
semiclassical trace formmulae, gross-shell effects in bound fermion systems can
be interpreted in terms of a few periodic orbits of the corresponding classical
systems. In integrable systems, these are usually the shortest members of the
most degenerate families or orbits, but in some systems also less degenerate
orbits can determine the gross-shell structure. Applications to nuclei, metal
clusters, semiconductor nanostructures, and trapped dilute atom gases are
discussed.Comment: LaTeX (revteX4) 6 pages; invited talk at Int. Conference "Finite
Fermionic Systems: Nilsson Model 50 Years", Lund, Sweden, June 14-18, 200
Phase-shift analysis of low-energy elastic-scattering data
Using electromagnetic corrections previously calculated by means of a
potential model, we have made a phase-shift analysis of the
elastic-scattering data up to a pion laboratory kinetic energy of 100 MeV. The
hadronic interaction was assumed to be isospin invariant. We found that it was
possible to obtain self-consistent databases by removing very few measurements.
A pion-nucleon model was fitted to the elastic-scattering database obtained
after the removal of the outliers. The model-parameter values showed an
impressive stability when the database was subjected to different criteria for
the rejection of experiments. Our result for the pseudovector
coupling constant (in the standard form) is . The six
hadronic phase shifts up to 100 MeV are given in tabulated form. We also give
the values of the s-wave scattering lengths and the p-wave scattering volumes.
Big differences in the s-wave part of the interaction were observed when
comparing our hadronic phase shifts with those of the current GWU solution. We
demonstrate that the hadronic phase shifts obtained from the analysis of the
elastic-scattering data cannot reproduce the measurements of the
charge-exchange reaction, thus corroborating past evidence that the hadronic
interaction violates isospin invariance. Assuming the validity of the result
obtained within the framework of chiral perturbation theory, that the mass
difference between the - and the -quark has only a very small effect on
the isospin invariance of the purely hadronic interaction, the
isospin-invariance violation revealed by the data must arise from the fact that
we are dealing with a hadronic interaction which still contains residual
effects of electromagnetic origin.Comment: 43 pages, 6 figure
Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking
We develop a uniform semiclassical trace formula for the density of states of
a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term
. This term breaks the U(3) symmetry of the HO, resulting in a
spherical system with SO(3) symmetry. We first treat the anharmonic term in
semiclassical perturbation theory by integration of the action of the perturbed
periodic HO orbits over the manifold P which characterizes
their 4-fold degeneracy. Then we obtain an analytical uniform trace formula
which in the limit of strong perturbations (or high energy) asymptotically goes
over into the correct trace formula of the full anharmonic system with SO(3)
symmetry, and in the limit (or energy) restores the HO trace
formula with U(3) symmetry. We demonstrate that the gross-shell structure of
this anharmonically perturbed system is dominated by the two-fold degenerate
diameter and circular orbits, and {\it not} by the orbits with the largest
classical degeneracy, which are the three-fold degenerate tori with rational
ratios of radial and angular frequencies. The same
holds also for the limit of a purely quartic spherical potential .Comment: LaTeX (revtex4), 26pp., 5 figures, 1 table; final version to be
published in J. Phys. A (without appendices C and D
Simple Analytical Particle and Kinetic Energy Densities for a Dilute Fermionic Gas in a d-Dimensional Harmonic Trap
We derive simple analytical expressions for the particle density
and the kinetic energy density for a system of noninteracting
fermions in a dimensional isotropic harmonic oscillator potential. We test
the Thomas-Fermi (TF, or local-density) approximation for the functional
relation using the exact and show that it locally
reproduces the exact kinetic energy density , {\it including the shell
oscillations,} surprisingly well everywhere except near the classical turning
point. For the special case of two dimensions (2D), we obtain the unexpected
analytical result that the integral of yields the {\it
exact} total kinetic energy.Comment: 4 pages, 4 figures; corrected versio
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