Semiclassical Density Of States Research Articles

Comparative quantum and semiclassical analysis of atom-field systems. I. Density of states and excited-state quantum phase transitions

We study the non-integrable Dicke model, and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semi-classical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semi-classical density of states, one {\em static} ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semi-classical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semi-classical result describes very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore the semi-classical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.

Quantum magneto-oscillations in the ac conductivity of disordered graphene

The dynamic conductivity \sigma(\omega) of graphene in the presence of diagonal white noise disorder and quantizing magnetic field B is calculated. We obtain analytic expressions for \sigma(\omega) in various parametric regimes ranging from the quasiclassical Drude limit corresponding to strongly overlapping Landau levels (LLs) to the extreme quantum limit where the conductivity is determined by the optical selection rules of the clean graphene. The nonequidistant LL spectrum of graphene renders its transport characteristics quantitatively different from conventional 2D electron systems with parabolic spectrum. Since the magnetooscillations in the semiclassical density of states are anharmonic and are described by a quasi-continuum of cyclotron frequencies, both the ac Shubnikov-de Haas oscillations and the quantum corrections to \sigma(\omega) that survive to higher temperatures manifest a slow beating on top of fast oscillations with the local energy-dependent cyclotron frequency.Both types of quantum oscillations possess nodes whose index scales as \omega^2. In the quantum regime of separated LLs, we study both the cyclotron resonance transitions, which have a rich spectrum due to the nonequidistant spectrum of LLs, and disorder-induced transitions which violate the clean selection rules of graphene. We identify the strongest disorder-induced transitions in recent magnetotransmission experiments. We also compare the temperature- and chemical potential-dependence of \sigma(\omega) in various frequency ranges from the dc limit allowing intra-LL transition only to the universal high-frequency limit where the Landau quantization provides a small B-dependent correction to the universal value of the interband conductivity \sigma=e^2/4 \hbar of the clean graphene.

Bose–Einstein condensation of noninteracting charged Bose gas in the presence of external potentials

We investigate thermodynamic properties of noninteracting charged bosons in the presence of externally applied electric and magnetic fields. Using the semiclassical density of states, we obtain the condensate fraction, chemical potential, total energy, and specific heat of a system of finite number of charged Bose particles. We conclude that Bose–Einstein condensation of the charged Bose gas occurs in the crossed electric and magnetic fields.

Semiclassical density of states at symmetric pitchfork bifurcations in coupled quartic oscillators.

We analyze the quantum density of states for a system of coupled quartic oscillators in the vicinity of symmetric isochronous or pitchfork bifurcations of the primary oscillator modes. A uniform semiclassical expression for the contribution to the density of states from the set of periodic orbits involved in the bifurcation is derived following the approach of Ozorio de Almeida and Hannay [J. Phys. A 20, 5873 (1987)] and Ozorio de Almeida and Aguiar [Physica D 41, 391 (1990)].

On the semiclassical density of states of quasi-integrable mechanical systems

For a class of quasi-integrable mechanical systems, we show that in the semiclassical limit the Bohr-Sommerfeld quantization applied to successive truncations of the Birkhoff series and a power series expansion of Weyl's formula give the same asymptotic number of states below a given energy.

Periodic orbits and a correlation function for the semiclassical density of states

Through the rule that there is one quantum state per Planck cell in phase space, classical mechanics supplies an ‘average’ semiclassical density of states for a system with bound motion. Can it supply more refined ‘averages’ such as the correlation function for the density of states ? I shall argue that for the two extreme cases of integrable classical motion and ergodic classical motion information can indeed be obtained on not quite this, but a closely related correlation function. The results for the two types of motion are markedly different.