Hybrid phase at the quantum melting of the Wigner crystal

We study the quantum melting of the two-dimensional Wigner crystal using a fixed node quantum Monte Carlo approach. In addition to the two already known phases (Fermi liquid at large density and Wigner crystal at low density), we find a third stable phase at intermediate values of the density. The third phase has hybrid behaviors in between a liquid and a solid. This hybrid phase has the nodal structure of a Slater determinant constructed out of the bands of a triangular lattice.     

Zero field Wigner crystal

A candidate for the insulating phase of the 2D electron gas, seen in high mobility 2D MOSFETS and heterojunctions, is a Wigner crystal pinned by the incipient disorder. With this in view, we study the effect of collective pinning on the physical properties of the crystal formed in zero external magnetic field. We use an elastic theory to describe to long wavelength modes of the crystal. The disorder is treated using the standard Gaussian variational method. We calculate various physical properties of the system with particular emphasis on their density dependence. We revisit the problem of compressibility in this system and present results for the compressibility obtained via effective capacitance measurements in experiments using bilayers. We present results for the dynamical conductivity, surface acoustic wave anomalies and the power radiated by the crystal through phonon emission at finite temperatures.     

One-dimensional Wigner crystal?

The linear response in a charge density wave (CDW) type state is investigated in the framework of 1+1-dimensional QED. It is shown that the system is unstable or stable against static, periodic electric perturbations when the Fermi level is placed in an allowed band or a forbidden one, respectively.     

Structure of the Wigner crystal

A model of the Wigner crystal with two localized electrons per cell is developed. The ground state energy of this model is evaluated. The Coulomb interaction within a cell is treated exactly for a certain range of electron concentrations. The calculation demonstrates that at very low electron concentrations the crystal contains a single localized electron per cell. As the concentration is increased the crystal comes to contain two, three or more electrons per cell. At high electron concentrations the entire crystal can be treated as a single cell.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp 47–51, June, 1988.     

Wigner crystal in snaked nanochannels

We study the properties of a Wigner crystal in snaked nanochannels and show that they are characterized by a conducting sliding phase at low charge densities and an insulating pinned phase above a critical charge density. The transition between these phases has a devil’s staircase structure typical for the Aubry transition in dynamical maps and the Frenkel-Kontorova model. We discuss the implications of this phenomenon for charge density waves in quasi-one-dimensional organic conductors and for supercapacitors in nanopore materials.     

Wigner dynamics of quantum semi-relativistic oscillator

The integral Wigner–Liouville equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte Carlo procedure and molecular dynamics methods. The strong influence of the relativistic effects on the time evolution of the momentum, velocity and coordinate Wigner distribution functions and the average values of quantum operators have been studied. Unexpected ‘protuberances’ in time evolution of the distribution functions were observed. Relativistic proper time dilation for oscillator have been calculated.     

Two-dimensional Wigner crystal in magnetic fields

Orbital magnetic moment and the frequency dependent conductivities of the Wigner crystal are examined in the harmonic approximation. The effects of scattering on the collective modes are also discussed.     

从离散Wigner函数的角度探讨量子相干性度量

量子相干性是量子信息处理的基本要素,在量子计算中扮演着重要的角色.为了便于讨论量子相干性在量子计算中的作用,本文从离散Wigner函数角度对量子相干性进行了探讨.首先对奇素数维量子系统的离散Wigner函数进行了分析,分离出表征相干性的部分,提出了一种可能的基于离散Wigner函数的量子相干性度量方法,并对其进行了量子相干性度量规范的分析;同时也比较了该度量与l_1范数相干性度量之间的关系.重要的是,这种度量方法能够明确给出量子相干性程度与衡量量子态量子计算加速能力的负性和之间不等式关系,由此可以解析地解释量子相干性仅是量子计算加速的必要条件.     

Wigner distribution of elliptical quantum optical vortex

We calculate the Wigner quasiprobability distribution function of the quantum elliptical vortex in elliptical beam (EEV), produced by coupling squeezed coherent states of two modes. The coupling between the two modes is performed by using beam splitter (BS) or a dual channel directional coupler (DCDC). The quantum interference due to the coupling between the two modes promises the generation of controlled entanglement for quantum computation and quantum tomography.     

Orbital magnetic moment of two-dimensional Wigner crystal

The orbital magnetic moment is calculated for the two-dimensional Wigner crystal within the harmonic approximation. It is shown that the temperature dependence of the magnetic moment in the crystalline state is in the marked contrast with that of the liquid state.     

Wigner functions and quantum interference in optics

A new, approximate generalized Wigner function based on discrete coherent state superpositions is introduced. It is shown that in contrast to the exact generalized Wigner function that may not exist in some region of its parameter the proposed approximate function exists everywhere.     

Wigner crystal in snaked nanochannels: Outlook

We study properties of Wigner crystal in snaked nanochannels and show that they are characterized by a conducting sliding phase at low charge densities and an insulating pinned phase emerging above a certain critical charge density. We trace parallels between this model problem and the Little suggestion for electron transport in organic molecules. We also show that in the presence of periodic potential inside the snaked channel the sliding phase exists only inside a certain window of electron densities that has similarities with a pressure dependence of conductivity in organic conductors. Our studies show emergence of dynamical glassy phase in a purely periodic potential in the absence of any disorder that can explain enormously slow variations of resistivity in organic conductors. Finally we discuss the KAM concept of superfluidity induced by repulsive Coulomb interaction between electrons. We argue that the transition from the sliding KAM phase to the pinned Aubry phase corresponds to the superfluid-insulator transition.     

Polarization catastrophe in the polaronic Wigner crystal

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a polaronic Wigner crystal at zero temperature, taking into account the quantum fluctuations of the polarization within the Feynman harmonic approximation. We show that, contrary to the ordinary electron crystal, the system undergoes a polarization catastrophe when the density is increased. An optical signature of this instability is derived, whose trend agrees with the experiments carried out in Nd-based cuprates. Received 4 July 2002 Published online 17 September 2002