Phase Transitions in Quantum Dots

We perform Hartree-Fock calculations to show that quantum dots (i.e. two dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. We tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wavefunction and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, we also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states.Comment: 14 pages, 7 postscript figure

Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations

A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter direction. This multilevel approach systematically implements a simple blocking strategy in a recursive manner to synthesize the sign cancellations among different fermionic paths throughout the whole configuration space. The practical usefulness of the method is demonstrated for interacting electrons in a quantum dot.Comment: 4 pages RevTeX, incl. two figure

Possible evidence for an inverted temperature-density relation in the intergalactic medium from the flux distribution of the Lyman-alpha forest

We compare the improved measurement of the Lya forest flux probability distribution at 1.7<z<3.2 presented by Kim et al. (2007) to a large set of hydrodynamical simulations of the Lya forest with different cosmological parameters and thermal histories. The simulations are in good agreement with the observational data if the temperature-density relation for the low density intergalactic medium (IGM), T=T_0 Delta^{gamma-1}, is either close to isothermal or inverted (gamma<1). Our results suggest that the voids in the IGM may be significantly hotter and the thermal state of the low density IGM may be substantially more complex than is usually assumed at these redshifts. We discuss radiative transfer effects which alter the spectral shape of ionising radiation during the epoch of HeII reionisation as a possible physical mechanism for achieving an inverted temperature-density relation at z~3.Comment: 16 pages, 6 figures, accepted for publication in MNRAS following minor revision. The accepted version includes an expanded discussion of the flux power spectru

Enhanced Acoustic Transmission Into Dissipative Solid Materials Through The Use Of Inhomogeneous Plane Waves

A number of applications, for instance ultrasonic imaging and nondestructive testing, involve the transmission of acoustic energy across fluid–solid interfaces into dissipative solids. However, such transmission is generally hindered by the large impedance mismatch at the interface. In order to address this problem, inhomogeneous plane waves were investigated in this work for the purpose of improving the acoustic energy transmission. To this end, under the assumption of linear hysteretic damping, models for fluid–structure interaction were developed that allow for both homogeneous and inhomogeneous incident waves. For low-loss solids, the results reveal that, at the Rayleigh angle, a unique value of the wave inhomogeneity can be found which minimizes the reflection coefficient, and consequently maximizes the transmission. The results also reveal that with sufficient dissipation levels in the solid material, homogeneous incident waves yield lower reflection values than inhomogeneous waves, due to the large degrees of inhomogeneity inherent in the transmitted waves. Analytical conditions have also been derived which predict the dependence of the optimal incident wave type on the dissipation level and wave speeds in the solid medium. Finally, implications related to the use of acoustic beams of limited spatial extent are discussed

Use of Evanescent Plane Waves for Low-Frequency Energy Transmission Across Material Interfaces

The transmission of sound across high-impedance difference interfaces, such as an air-water interface, is of significant interest for a number of applications. Sonic booms, for instance, may affect marine life, if incident on the ocean surface, or impact the integrity of existing structures, if incident on the ground surface. Reflection and refraction at the material interface, and the critical angle criteria, generally limit energy transmission into higher-impedance materials. However, in contrast with classical propagating waves, spatially decaying incident waves may transmit energy beyond the critical angle. The inclusion of a decaying component in the incident trace wavenumber yields a nonzero propagating component of the transmitted surface normal wavenumber, so energy propagates below the interface for all oblique incident angles. With the goal of investigating energy transmission using incident evanescent waves, a model for transmission across fluid-fluid and fluid-solid interfaces has been developed. Numerical results are shown for the air-water interface and for common air-solid interfaces. The effects of the incident wave parameters and interface material properties are also considered. For the air-solid interfaces, conditions can be found such that no reflected wave is generated, due to impedance matching among the incident and transmitted waves, which yields significant transmission increases over classical incident waves

On The Use Of Evanescent Plane Waves For Low-Frequency Energy Transmission Across Material Interfaces

The transmission of airborne sound into high-impedance media is of interest in several applications. For example, sonic booms in the atmosphere may impact marine life when incident on the ocean surface, or affect the integrity of existing structures when incident on the ground. Transmission across high impedance-difference interfaces is generally limited by reflection and refraction at the surface, and by the critical angle criterion. However, spatially decaying incident waves, i.e., inhomogeneous or evanescent plane waves, may transmit energy above the critical angle, unlike homogeneous plane waves. The introduction of a decaying component to the incident trace wavenumber creates a nonzero propagating component of the transmitted normal wavenumber, so energy can be transmitted across the interface. A model of evanescent plane waves and their transmission across fluid-fluid and fluid-solid interfaces is developed here. Results are presented for both air-water and air-solid interfaces. The effects of the incident wave parameters (including the frequency, decay rate, and incidence angle) and the interfacial properties are investigated. Conditions for which there is no reflection at the air-solid interface, due to impedance matching between the incident and transmitted waves, are also considered and are found to yield substantial transmission increases over homogeneous incident waves

The Construction of Acoustic Waveforms from Plane Wave Components to Enhance Energy Transmission into Solid Media

The transmission of acoustic energy into solid materials is of interest in a wide range of applications, including ultrasonic imaging and nondestructive testing. However, the large impedance mismatch at the solid interface generally limits the transmission of incident acoustic energy. With the goal of improving the fraction of the energy transmitted into solid materials, the use of various bounded spatial profiles, including commonly-employed forms, such as Gaussian distributions, as well as newly-constructed profiles, has been investigated. The spatial profile is specified as the pressure amplitude distribution of the incident wave. Bounded acoustic beams are represented here as sums of harmonic plane waves, and results obtained for the optimal parameters of incident plane wave components are used to inform the construction of bounded wave profiles. The effect of the form of the spatial profile is investigated, with the total energy carried by the incident wave held constant as the profile is varied, and the relationship with the plane wave components which superimpose to form the bounded wave is discussed. Direct comparisons are made for the efficiency of the energy transmission of different profiles. The results reveal that, by tuning the form of the profile, substantial improvements in the total energy transmission can be achieved as compared to Gaussian and square waveforms

Low-Frequency Energy Transmission across Material Interfaces using Incident Evanescent Waves

Transmission of airborne sound into higher-impedance materials is of interest in a range of applications. Sonic booms, for example, may adversely affect marine life, if incident on the ocean surface, or may produce underground pressure waves potentially capable of impacting the integrity of existing structures, if incident on the ground surface. Energy transmission into higher-impedance materials is generally limited by significant reflection and refraction at the material interface, and by the critical angle criteria. However, unlike classical waves, spatially-decaying, or evanescent, incident waves can transmit energy at angles beyond the critical angle. When a decaying component is introduced into the incident trace wavenumber, the interaction at the interface produces a nonzero propagating component of the transmitted surface normal wavenumber, so energy is transmitted across the interface for all oblique incident angles. With the aim of investigating energy transmission using incident evanescent waves, a model for pressure and intensity transmission across the fluid-fluid and fluid-solid interfaces has been developed. Numerical results are given for common interfaces that include the air-water interface and typical air-solid interfaces, where the effects of the incident wave parameters and interface material properties are considered as well. For the air-solid interfaces, conditions can be tuned such that no reflected wave is generated at the interface, owing to impedance matching between the incident and transmitted waves, which yields considerable transmission increases over classical incident waves

Stress and Energy Transmission by Inhomogeneous Plane Waves into Dissipative Media

The characteristics of sound transmission into real, or dissipative, media differ from those of transmission into lossless media. In particular, when a plane wave in a fluid is incident upon a real, dissipative elastic material, the transmitted waves are in general inhomogeneous, even when the incident wave is itself homogeneous and incident at a sub-critical angle; and more significantly, energy transmission occurs even above the critical angle. In addition, for any real incidence angle, the parameters of an incident inhomogeneous wave may be tuned so that there is no reflection from the surface of a viscoelastic solid. That phenomenon may be exploited in applications requiring energy transmission into solids. In this work, the transmission of incident inhomogeneous, as well as homogeneous, acoustic waves into solid materials is characterized; a hysteretic damping model is assumed. Numerical results are presented for the transmitted stress and energy distributions for typical solid materials, including polymer-based solids. The conditions for total transmission, i.e., no reflection at the interface, are explored, where the propagation angle, degree of inhomogeneity, and frequency of the incident wave are varied for a given material. These investigations show substantial transmission gains in the vicinity of the zero of the reflection coefficient, compared to homogeneous incident waves

Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover only governed by the density parameter $r_s$. For $r_s>r_c$, the data are consistent with a Wigner molecule description, while for $r_s<r_c$, Fermi liquid behavior is recovered. The crossover value $r_c \approx 4$ is surprisingly small.Comment: 4 pages RevTeX, 3 figures, corrected Tabl