A one-dimensional (1D) Bose system with dipole-dipole repulsion is studied at zero temperature by means of a Quantum Monte Carlo method. It is shown that in the limit of small linear density the bosonic system of dipole moments acquires many properties of a system of non-interacting fermions. At larger linear densities a Variational Monte Carlo calculation suggests a crossover from a liquidlike to a solid-like state. The system is superfluid on the liquid-like side of the crossover and is normal in the deep on the solid-like side. Energy and structural functions are presented for a wide range of densities. Possible realizations of the model are 1D Bose atom systems with permanent dipoles or dipoles induced by static field or resonance radiation, or indirect excitons in coupled quantum wires, etc. We propose parameters of a possible experiment and discuss manifestations of the zero-temperature quantum crossover.Up until now Bose-Einstein condensation has been realized in many different atom and molecule species with short-range interactions. At low temperatures such an interaction can be described by a s-wave scattering length and is commonly approximated by a contact pseudopotential. In contrast, some recent work has focused on the realization of dipole condensates [1,2,3,4,5]. In these systems, the dipole-dipole interaction extends to much larger distances and significant differences in the properties (such as the phase diagram and correlation functions) are expected. Another appealing aspect of a system of dipole moments is the relative ease of tuning the effective strength of interactions [6] which makes the system highly controllable. Dipole particles are also considered to be a promising candidate for the implementation of quantum-computing schemes [7,8,9].On the theoretical side dipole condensates have been mainly studied on a semiclassical (Gross-Pitaevskii) [10] or Bogoliubov [11] level. A model Bose-Hubbard Hamiltonian has been used to describe a dipole gas in optical lattices and a rich phase diagram was found [5,12]. So far there have been no full quantum microscopic computations of the properties of a homogeneous system.Recently the Monte Carlo method was used to study helium and molecular hydrogen in nanotubes [13]. Such a geometry, which is effectively one dimensional, leads to completely different properties compared to a threedimensional sample.We consider N repulsive dipole moments of mass M located on a line. The Hamiltonian of such a system is given bŷWe keep in mind two different possible realizations: 1) Cold bosonic atoms, with induced or static dipole momenta, in a transverse trap so tight that excitations of the levels of the transverse confinement are not possible and the system is dynamically one-dimensional. The dipoles themselves can be either induced or permanent. In the case of dipoles induced by an electric field E the coupling has the form C dd = E 2 α 2 , where α is the static polarizability. For permanent magnetic dipoles aligned by an external magnetic field one has C dd = m 2 ...
We demonstrate a new method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum WignerLiouville equation. These classical trajectories obey Hamilton-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.
We develop a representation of quantum states in which the states are described by fair probability distribution functions instead of wave functions and density operators. We present a one-random-variable tomography map of density operators onto the probability distributions, the random variable being analogous to the center-of-mass coordinate considered in reference frames rotated and scaled in the phase space. We derive the evolution equation for the quantum state probability distribution and analyze the properties of the map. To illustrate the advantages of the new tomography representations, we describe a new method for simulating nonstationary quantum processes based on the tomography representation. The problem of the nonstationary tunneling of a wave packet of a composite particle, an exciton, is considered in detail.
The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function (quantum tomogram). In the framework of the method one uses the ensemble of trajectories in the tomographic space to represent evolution of the system (therefore direct calculation of the quantum tomogram is avoided). To illustrate the method we consider the problem of nonstationary tunneling of a wave packet. Different characteristics of tunneling, such as tunneling time, evolution of spatial and momentum distributions, tunneling probability are calculated in the quantum tomography approach. Tunneling of a wave packet of composite particle, exciton, is also considered; exciton ionization due to the scattering on the barrier is analyzed.Comment: 10 pages, 10 figures, submitted to Phys. Rev.
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