Closed-orbit theory for spatial density oscillations

We briefly review a recently developed semiclassical theory for quantum oscillations in the spatial (particle and kinetic energy) densities of finite fermion systems and present some examples of its results. We then discuss the inclusion of correlations (finite temperatures, pairing correlations) in the semiclassical theory.Comment: LaTeX, 10pp., 2 figure

Anomalous shell effect in the transition from a circular to a triangular billiard

We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shell effect emerges from a codimension-two bifurcation of the triangular periodic orbit. Gutzwiller's semiclassical trace formula, using a global uniform approximation for the bifurcation of the triangular orbit and including the contributions of the other isolated orbits, describes very well the coarse-grained quantum-mechanical level density of this system. We also discuss the role of discrete symmetry for the large shell effect obtained here.Comment: 14 pages REVTeX4, 16 figures, version to appear in Phys. Rev. E. Qualities of some figures are lowered to reduce their sizes. Original figures are available at http://www.phys.nitech.ac.jp/~arita/papers/tricirc

Closed orbits and spatial density oscillations in the circular billiard

We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed periodic and non-periodic orbits. We discuss their bifurcations under variation of the starting point r and derive analytical expressions for their properties such as actions, stability determinants, momentum mismatches and Morse indices. We present semiclassical calculations of the spatial density oscillations using a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev. Lett. 100 200408], employing standard uniform approximations from perturbation and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final version (v3) to be published in J. Phys.

Super-shell structure in harmonically trapped fermionic gases and its semi-classical interpretation

It was recently shown in self-consistent Hartree-Fock calculations that a harmonically trapped dilute gas of fermionic atoms with a repulsive two-body interaction exhibits a pronounced {\it super-shell} structure: the shell fillings due to the spherical harmonic trapping potential are modulated by a beat mode. This changes the ``magic numbers'' occurring between the beat nodes by half a period. The length and amplitude of the beating mode depends on the strength of the interaction. We give a qualitative interpretation of the beat structure in terms of a semiclassical trace formula that uniformly describes the symmetry breaking U(3) $\to$ SO(3) in a 3D harmonic oscillator potential perturbed by an anharmonic term $\propto r^4$ with arbitrary strength. We show that at low Fermi energies (or particle numbers), the beating gross-shell structure of this system is dominated solely by the two-fold degenerate circular and (diametrically) pendulating orbits.Comment: Final version of procedings for the 'Nilsson conference

Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry

Deformed shell structures in nuclear mean-field potentials are systematically investigated as functions of deformation and surface diffuseness. As the mean-field model to investigate nuclear shell structures in a wide range of mass numbers, we propose the radial power-law potential model, V \propto r^\alpha, which enables a simple semiclassical analysis by the use of its scaling property. We find that remarkable shell structures emerge at certain combinations of deformation and diffuseness parameters, and they are closely related to the periodic-orbit bifurcations. In particular, significant roles of the "bridge orbit bifurcations" for normal and superdeformed shell structures are pointed out. It is shown that the prolate-oblate asymmetry in deformed shell structures is clearly understood from the contribution of the bridge orbit to the semiclassical level density. The roles of bridge orbit bifurcations in the emergence of superdeformed shell structures are also discussed.Comment: 20 pages, 23 figures, revtex4-1, to appear in Phys. Rev.

Loschmidt echo decay from local boundary perturbations

We investigate the sensitivity of the time evolution of semiclassical wave packets in two-dimensional chaotic billiards with respect to local perturbations of their boundaries. For this purpose, we address, analytically and numerically, the time decay of the Loschmidt echo (LE). We find the LE to decay exponentially in time, with the rate equal to the classical escape rate from an open billiard obtained from the original one by removing the perturbation-affected region of its boundary. Finally, we propose a principal scheme for the experimental observation of the LE decay.Comment: Final version; 4 pages, 3 figure

A semiclassical analysis of the Efimov energy spectrum in the unitary limit

We demonstrate that the (s-wave) geometric spectrum of the Efimov energy levels in the unitary limit is generated by the radial motion of a primitive periodic orbit (and its harmonics) of the corresponding classical system. The action of the primitive orbit depends logarithmically on the energy. It is shown to be consistent with an inverse-squared radial potential with a lower cut-off radius. The lowest-order WKB quantization, including the Langer correction, is shown to reproduce the geometric scaling of the energy spectrum. The (WKB) mean-squared radii of the Efimov states scale geometrically like the inverse of their energies. The WKB wavefunctions, regularized near the classical turning point by Langer's generalized connection formula, are practically indistinguishable from the exact wave functions even for the lowest ($n=0$) state, apart from a tiny shift of its zeros that remains constant for large $n$.Comment: LaTeX (revtex 4), 18pp., 4 Figs., already published in Phys. Rev. A but here a note with a new referece is added on p. 1

Finite size corrections to the blackbody radiation laws

We investigate the radiation of a blackbody in a cavity of finite size. For a given geometry, we use semiclassical techniques to obtain explicit expressions of the modified Planck's and Stefan-Boltzmann's blackbody radiation laws as a function of the size and shape of the cavity. We determine the range of parameters (temperature, size and shape of the cavity) for which these effects are accessible to experimental verification. Finally we discuss potential applications of our findings in the physics of the cosmic microwave background and sonoluminescence.Comment: 5 pages, 1 figure, journal versio