Quantum groups of fermionic algebras

We consider inhomogeneous quantum groups that transform various types of fermions: standard fermions, commuting fermions and orthofermions. These quantum groups are notq-deformations.     

Representation of orthofermion spin operators

The algebraic expressions for the total spin operators expressed in terms of orthofermion creation and annihilation operators are combined into a single equation. The terms in this expressions are rearranged to provide representations of local spin operators. This task is essential for modelling a system of orthofermions in the presence of a magnetic field. By factorizing the orthofermion annihilation (creation) operators into charge and spin dependent parts, it is shown that the latter part suffices to represent spin number, raising and lowering operators. Finally a connection is provided between the spin systems and Greenberg’s infinite statistics.     

Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, pre-formed Cooper pairs in chemical/thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the Bose-Einstein condensation (BEC) singularity temperature T_c is approached from above. Compared with BCS theory (which is not a BEC theory) substantially higher T_cs are obtained without any adjustable parameters, that fall roughly within the range of empirical T_cs for quasi-2D cuprate superconductors.     

A new interpretation for orthofermions

In this article we introduce a simple physical model which realizes the algebra of orthofermions. The model is constructed from a cylinder which can be filled with some balls. The creation and annihilation operators of orthofermions are related to the creation and annihilation operators of balls in certain positions in the cylinder. Relationship between this model and topological symmetries in quantum mechanics is investigated.     

Ideal bose gas in an oscillator potential (exact solution)

Exact expressions for the statistical sum of the grand canonical ensemble and the one-particle density matrix are derived based on the definition of the density matrix for a system of N identical noninteracting Bose particles in an oscillator potential as a sum with respect to the symmetric exchange of the density matrix coordinates of distinguishable particles. A quasi-classical scenario is analyzed in detail.     

Conservation laws in the quantum Hall Liouvillian theory and its generalizations

It is known that the localization length scaling of noninteracting electrons near the quantum Hall plateau transition can be described in a theory of the bosonic density operators, with no reference to the underlying fermions. The resulting “Liouvillian” theory has a U(1|1) global supersymmetry as well as a hierarchy of geometric conservation laws related to the noncommutative geometry of the lowest Landau level (LLL). Approximations to the Liouvillian theory contain quite different physics from standard approximations to the underlying fermionic theory. Mean-field and large-N generalizations of the Liouvillian are shown to describe problems of noninteracting bosons that enlarge the U(1|1) supersymmetry to U(1|1)×SO(N) or U(1|1)×SU(N).These noninteracting bosonic problems are studied numerically for 2⩽N⩽8 by Monte Carlo simulation and compared to the original N=1 Liouvillian theory. The N>1 generalizations preserve the first two of the hierarchy of geometric conservation laws, leading to logarithmic corrections at order 1/N to the diffusive large-N limit, but do not preserve the remaining conservation laws. The emergence of nontrivial scaling at the plateau transition, in the Liouvillian approach, is shown to depend sensitively on the unusual geometry of Landau levels.     

Optical properties of semiconducting carbon nanotubes under axial magnetic field

The linear polarizability absorption spectra of semiconducting carbon nanotubes under axial magnetic field (B) have been calculated by the π-orbital tight-binding model and sum-over-state method. We have found that the optical spectra are split by the B-induced symmetry breaking and the amount of splitting increases with increase of magnetic field. Although the results are obtained within the noninteracting tight-binding model, the amount of splitting is still consistent with the experimental observation, offering a fast estimation of the B-induced splitting. Our numerical results also indicate that the splitting amounts of the second and third absorption peaks are close to that of the first one, which may be observed by the future experiments.     

Some remarks on the time-dependent Thomas-Fermi theory

We investigate the Thomas Fermi limit (?=0) of the density operator in phase space for a system of noninteracting fermions evolving from the ground state in a time dependent potential. The semiclassical calculations for model situations in one spatial dimension are compared with the solution of the time dependent Schrödinger equation. The role of time dependent invariants and the relation to the hydrodynamical formulation of quantum mechanics is pointed out.     

Persistence of quantum information

We study the flip-processes in a two-level system, which is triggered by the coupling to a classical bath. When the bath is represented by a stochastic field, the time evolution of the density matrix leads to a stochastic equation with a multiplicative noise. Accordingly the Fokker–Planck-equation (FPE) depends on the matrix elements of the underlying density operator. The solution of the FPE can be parametrized in terms of an inherent conserved quantity α, which is interpreted as a measure for the persistence of quantum information. We show that the FPE exhibits a single unique steady state solution different from Boltzmann's law. The exactly computable discrete spectrum of the relaxation times is characterized by two quantum numbers and the ratio of Planck's constant and the coupling strength to the bath. The total entropy is analyzed as function of the quantum number α  . In case of α=1$\alpha =1$ the system is in a pure state whereas for α≠1$\alpha \ne 1$ a mixed state is realized. In case of two, two-level systems, immersed in the common bath, the two noninteracting two-level systems become mutually entangled. The annealed entropy is in that case non-extensive.     

Controlling entanglement sudden death and birth in cavity QED

We present a scheme to control the entanglement sudden birth and death in a cavity quantum electrodynamics system, which consists of two noninteracting atoms each locally interacting with its own vacuum field, by applying and adjusting classical driving fields.     

Tunneling of two interacting electrons in a quantum wire

A model calculation is reported for the tunneling probability of one as well as two interacting electrons from a quantum well within a narrow channel. We discuss the cases when the two electrons are spin polarized or unpolarized by transforming the system to a noninteracting one with the use of quantal density functional theory to obtain an effective single-particle confining potential. A semiclassical approach is used to obtain the tunneling probability from this effective potential. The calculation is motivated by recent measurements of the conductance of an electron gas in a narrow channel but is not meant to explain the anomalous behavior that has been reported since, for example, we deal with a simplified two-level system. Numerical results for the tunneling probability are presented.     

Phase separation and d-wave superconductivity induced by extended electron–exciton interaction

Using an auxiliary-field quantum Monte Carlo (AFQMC) method, we have studied a two-dimensional tight-binding model in which the conduction electrons can polarize an adjacent layer of molecules through electron–electron repulsion. Calculated average conduction electron density as a function of chemical potential exhibits a clear break characteristic of phase separation. Compared to the noninteracting system, the d-wave pair-field correlation function shows significant enhancement. The simultaneous presence of phase separation and d-wave superconductivity suggests that an effective extended pairing force is induced by the electron–exciton coupling.     

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation(ME) approach under the self-consistent Born approximation(SCBA) for quantum transport through mesoscopic systems.The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations.The proposed n-SCBA-ME goes beyond the scope of the BornMarkov master equation,being applicable to transport under small bias voltage,in non-Markovian regime and with strong Coulomb correlations.For steady state,it can recover not only the exact result of noninteracting transport under arbitrary voltages,but also the challenging nonequilibrium Kondo efect.Moreover,the n-SCBA-ME approach is efcient for the study of shot noise.We demonstrate the application by a couple of representative examples,including particularly the nonequilibrium Kondo system.     

Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.     

Generalization of Luttinger’s theorem for strongly correlated electron systems

By on the analyzing the general structure of the Green function of a strongly correlated electron system, it is shown that, for the regime of strong correlations, Luttinger’s theorem should be generalized in the following way: the volume of the Fermi surface of the system of noninteracting particles is equal to that of the quasiparticles in the strongly correlated system with due regard for the spectral weight of the quasiparticles. An investigation of the t-J model and of the Hubbard model, as applied to the paramagnetic nonsuperconducting phase, shows that the generalized Luttinger theorem is valid for these models.     

Entanglement and the Kondo effect in serially coupled double quantum dots

We investigate entanglement between electrons in serially coupled double quantum dots attached to noninteracting leads. In addition to local repulsion we consider the influence of capacitive inter-dot interaction. We show how the competition between extended Kondo and local singlet phases determines the ground state and thereby the entanglement. The results are additionally discussed in connection with the linear conductance through the system.     

High temperature collective spin-photon coupling in a microwave cavity

An ensemble of N noninteracting spins being in thermal equilibrium and coupled to the resonant mode of a lossless microwave cavity is studied as the function of the spin temperature τ. Near τ = 0 the system is known to be in a coupled spin-photon state that manifests itself by the splitting of the cavity mode (vacuum Rabi splitting). The cavity emission spectrum is simulated for arbitrary τ. A critical temperature τ _C = ω _S √N/2, where ω _S is the spin excitation energy, is related to the destruction of the strong coupling regime as a consequence of thermal excitations arising within the spin ensemble.     

Finite cell calculations on the periodic Anderson Hamiltonian

We report finite cell calculations on the one-dimensional periodic Anderson Hamiltonian. The ground state for two electrons per site is found to be an insulating non-magnetic singlet, which evolves continuously from the noninteracting U = 0 limit to the large U mixed valence and Kondo lattice regimes. The calculations for four sites given energy gaps which agree well with results for the infinite lattice in the few cases where they are known.     

On the exact mean-field description of continuous quantum systems in equilibrium

The thermodynamic limit of free energy density is investigated for quantum systems of n particles obeying Boltzmann, Fermi and Bose statistics, interacting via spin-independent 2-body bounded separable potentials and confined to a bounded region Λ ? R^v. The technique used exploits the Feynman-Kac theorem in finite volume and the saddle-point method of Tindemans and Capel. It is shown that the limiting free energy density of such systems is equal to that of a system of noninteracting particles subject to a mean field which is equal to the averaged 2-body interaction. The equations for the mean field of n particles obeying Boltzmann, Fermi or Bose statistics represent self-consistent field problems and their forms comply with the well-known theorems on mean occupation numbers of single-particle eigenstates of ideal quantum gases at inverse temperature β.