Rotating Fermi gases in an anharmonic trap

Motivated by recent experiments on rotating Bose-Einstein condensates, we investigate a rotating, polarized Fermi gas trapped in an anharmonic potential. We apply a semiclassical expansion of the density of states in order to determine how the thermodynamic properties depend on the rotation frequency. The accuracy of the semiclassical approximation is tested and shown to be sufficient for describing typical experiments. At zero temperature, rotating the gas above a given frequency Ω_DO leads to a ‘donut’-shaped cloud which is analogous to the hole found in two-dimensional Bose-Einstein condensates. The free expansion of the gas after suddenly turning off the trap is considered and characterized by the time and rotation frequency dependence of the aspect ratio. Temperature effects are also taken into account and both low- and high-temperature expansions are presented for the relevant thermodynamical quantities. In the high-temperature regime a virial theorem approach is used to study the delicate interplay between rotation and anharmonicity.     

Quadruply excited beryllium-like atoms – a semiclassical model

The semiclassical spectrum of quadruply highly excited four-electron atomic systems has been calculated for the plane model of equivalent electrons. The energy of the system consists of rotational and vibrational modes within the circular skeleton orbit approximation, as used in a previous calculation for the triply excited three-electron systems. The full dynamical analysis is carried out within the Hamiltonian theory, accounting for the inertial effects and the complete coupling between different degrees of freedom. Here we present numerical results for energy spectrum of the beryllium atom. The lifetimes of the semiclassical states are estimated via the corresponding Lyapunov exponents. The vibrational modes relative contribution to the energy levels rises with the degree of the Coulombic excitation.     

Oscillatory behavior and enhancement of the surface plasmon linewidth in embedded noble metal nanoparticles

We study the Landau damping of the surface plasmon resonance of metallic nanoparticles embedded in different environments of experimental relevance. Important oscillations of the plasmon linewidth as a function of the radius of the nanoparticles are obtained from numerical calculations based on the time dependent local density approximation. These size-oscillations are understood, within a semiclassical approximation, as a consequence of correlations in the spectral density of the nanoparticles. We treat inert matrices, as well as the case with an unoccupied conduction band. In the latter case, the plasmon lifetime is greatly reduced with respect to the inert case, but the non-monotonous size-dependence persists.     

The partition function of an interacting many body system

Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuations and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e.g. for gap fluctuations in nanoscale superconducting devices previously studied within a PSPA type of approximation. Received 28 March 2002 Published online 17 September 2002     

s-wave and p-wave scattering in a cold gas of Na and Rb atoms

Using improved experimentally based X¹Σ⁺ and a³Σ⁺ molecular potentials of NaRb, we apply the variable phase method to compute new data for low energy scattering of ²³Na atoms by ⁸⁵Rb atoms and ⁸⁷Rb atoms. These are the scattering lengths and volumes, numbers of bound states and effective ranges, which we use to obtain the low energy spin-change cross section as functions of the system temperature and the isotope masses. From an analysis of the contributions of s-wave and p-wave scatterings to the elastic cross section we estimate temperatures below which only s-wave scattering is dominant. We compare our quantal results to data obtained from the semiclassical approximation. We supply evidence for the existence of a near zero energy p-wave bound state supported by the singlet molecular potential.     

Corrections to Hawking-like radiation for a Friedmann–Robertson–Walker universe

Recently, a Hamilton–Jacobi method beyond the semiclassical approximation in black hole physics was developed by Banerjee and Majhi. We generalize their analysis of black holes to the case of a Friedmann–Robertson–Walker (FRW) universe. It is shown that all the higher order quantum corrections in the single particle action are proportional to the usual semiclassical contribution. The corrections to the Hawking-like temperature and entropy of the apparent horizon for the FRW universe are also obtained. In the corrected entropy, the area law involves a logarithmic area correction together with the standard term with the inverse power of the area.     

Semiclassical theory of molecular collisions: Real and complex-valued classical trajectories for collinear atom Morse oscillator collisions

Real and complex-valued classical trajectories have been calculated for the collinear collision of an atom with a Morse oscillator. They are used in three semiclassical approximations for the transition probability: a Bessel uniform approximation, an Airy uniform approximation and a primitive semiclassical approximation. Comparison with exact quantum results shows that the Bessel uniform approximation is accurate even for near elastic collisions where the Airy and primitive approximations break down. The Airy and Bessel approximations agree quite closely for inelastic collisions however. The primitive semiclassical approximation is less accurate than either the Airy or Bessel approximation.     

Semiclassical regime of Regge calculus and spin foams

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine—as expected from the semiclassical limit of spin foam models—then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.     

Finite temperature theory of metastable anharmonic potentials

The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a function of temperature. The family of classical paths, saddle points for the action, is derived in terms of Jacobian elliptic functions whose periodicity sets the energy-temperature correspondence. The period of the classical oscillations varies monotonically with the energy up to the sphaleron, pointing to a smooth crossover from the quantum to the activated regime. The softening of the quantum fluctuation spectrum is evaluated analytically by the theory of the functional determinants and computed at low T up to the crossover. In particular, the negative eigenvalue, causing an imaginary contribution to the partition function, is studied in detail by solving the Lamè equation which governs the fluctuation spectrum. For a heavvy particle mass, the decay rate shows a remarkable temperature dependence mainly ascribable to a low lying soft mode and, approaching the crossover, it increases by a factor five over the predictions of the zero temperature theory. Just beyond the peak value, the classical Arrhenius behavior takes over. A similar trend is found studying the quartic metastable potential but the lifetime of the latter is longer by a factor ten than in a cubic potential with same parameters. Some formal analogies with noise-induced transitions in classically activated metastable systems are discussed.     

Temperature dependence of atomic spectral line widths in a plasma

We investigated here temperature dependence of Stark widths for neutral atom spectral lines in order to find a more precise method for scaling with temperature than sometimes used dependence T^-1/2, which is often inadequate particularly for Stark broadening of neutral emitter lines. We found here an analytical scaling with temperature within simplified semiclassical approaches of Freudenstein and Cooper and Dimitrijević and Konjević. For analysis of the temperature dependence, lines of HeI were used.     

Tunneling spectra of submicron Bi<Subscript>2</Subscript>Sr<Subscript>2</Subscript>CaCu<Subscript>2</Subscript>O<Subscript>8+</Subscript><Subscript>δ</Subscript> intrinsic Josephson junctions: evolution from superconducting gap to pseudogap

The electronic, structural, and magnetic properties of Ru and Rh thin films on Ag(001) substrate are investigated by means of density functional calculations. The generalized gradient approximation is used to treat the exchange correlation potential. Alloying, burying, and fully relaxing effects are considered for different degrees of coverage: 0.25, 0.50, 1 and 2 ML. Alloying and burying effects reduce the magnetic moments while fully relaxing effects enlarge them. For Ru, the magnetic moment is high for 0.25 ML and vanishes for 2 ML; however, for Rh, the magnetic moment remains high even for 2 ML. Nevertheless, when cluster formation is analysed we conclude that the absence of magnetism in a number of previous experimental works could be attributed to the formation of big size clusters.     

Twofold-broken rational tori and the uniform semiclassical approximation

We investigate broken rational tori consisting of a chain of four (rather than two) periodic orbits. The normal form that describes this configuration is identified and used to construct a uniform semiclassical approximation, which can be utilized to improve trace formulae. An accuracy gain can be achieved even for the situation when two of the four orbits are ghosts. This is illustrated for a model system, the kicked top. Received 3 August 1999     

From semiclassical transport to quantum Hall effect under low-field Landau quantization

The crossover from the semiclassical transport to the quantum Hall effect is studied by examining a two-dimensional electron system in an AlGaAs/GaAs heterostructure. By probing the magneto-oscillations, it is shown that the semiclassical Shubnikov-de Haas (SdH) formulation can be valid even when the minima of the longitudinal resistivity approach zero. The extension of the applicable range of the SdH theory could be due to the damping effects resulting from disorder and temperature. Moreover, we observed plateau-plateau transition-like behavior with such an extension. From our study, it is important to include positive magnetoresistance to refine the SdH theory.     

Is Hawking temperature modified by the quantum tunneling beyond semiclassical approximation

Hawking temperature of a static and spherically symmetric black hole beyond semiclassical approximation is studied. The calculations show us that different definition of the particle’s energy gives different Hawking temperature. However, we argue that the result obtained using the standard definition of the particle energy is reasonable because it keeps the validity of the first law of the thermodynamics, i.e., both the Hawking temperature and entropy are not modified by the quantum tunneling beyond semiclassical approximation. The result shows us that any hypothetical (^h/_2p){\hbar} corrections to the tunneling rate are to be interpreted not as quantum corrections to the Hawking temperature but as fluctuations about a thermal background.     

Kinetics of quasiballistic transport in nanoscale semiconductor structures: is the ballistic limit attainable at room temperature?

Electron transport in nanoscale semiconductor structures is theoretically investigated to answer the question of whether or not the ballistic limit is really attainable under room temperature operation. The semiclassical Boltzmann transport equation is solved analytically under the relaxation time approximation for n(+)-n-n(+) test structures. We demonstrate that the solution of the Boltzmann transport equation exhibits a boundary layer structure near the potential barrier and thus the scatterings in the active region cannot be neglected even in nanoscale structures, as far as they are operated at room temperature under high applied voltages.     

Hadronic density of states from string theory

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nù?ez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.     

Bifurcation phenomena of photodetached electron flux in parallel external fields

A semiclassical method based on the closed-orbit theory is applied to analysing the dynamics of photodetached electron of H$^- $ in the parallel electric and magnetic fields. By simply varying the magnetic field we reveal spatial bifurcations of electron orbits at a fixed emission energy, which is referred to as the fold caustic in classical motion. The quantum manifestations of these singularities display a series of intermittent divergences in electronic flux distributions. We introduce semiclassical uniform approximation to repair the electron wavefunctions locally in a mixed phase space and obtain reasonable results. The approximation provides a better treatment of the problem.     

Thomas-Fermi approach to thermal quantum hadrodynamics

We present a relativistic, thermal Thomas-Fermi model, which we derive as the lowest-order contribution to the semiclassical expansion of the corresponding Hartree approximation of quantum hadrodynamics. It is used to study properties of hot symmetric as well as asymmetric nuclei, in relation to the critical behaviour of nuclear matter. In order to derive the surface coefficient for a finite temperature version of the liquid-drop model, we investigate properties of semi-infinite nuclear matter.