Semiclassical diagonalization of quantum Hamiltonian and equations of motion with Berry phase corrections

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order ħ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.     

Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems

The pairwise entanglement, measured by concurrence and geometric phase in high dimensional free-Fermion lattice systems have been studied in this paper. When the system stays at the ground state, their derivatives with the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-Fermion model that both concurrence and geometric phase show the intimate connection with the correlation functions. The possible connection between concurrence and geometric phase has been also discussed.     

The role of bound states in time-dependent quantum transport

Charge transport through a nanoscale junction coupled to two macroscopic electrodes is investigated for the situation when bound states are present. We provide numerical evidence that bound states give rise to persistent, non-decaying current oscillations in the junction. We also show that the amplitude of these oscillations can exhibit a strong dependence on the history of the applied potential as well as on the initial equilibrium configuration. Our simulations allow for a quantitative investigation of several transient features. We also discuss the existence of different timescales and address their microscopic origin.     

Conductance through analytic constrictions

We study the dependence of the intrinsic conductance of a nanocontact on its shape by using the recursion-transfer-matrix method. Hour-glass, torus, and spherical shapes are defined through analytic potentials, the latter two serving as rough models for ring-like and spherical molecules, respectively. The sensitivity of the conductance to geometric details is analyzed and discussed. Strong resonance effects are found for a spherical contact weakly coupled to electron reservoirs.     

Projection operator approach to transport in complex single-particle quantum systems

We discuss the time-convolutionless (TCL) projection operator approach to transport in closed quantum systems. The projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. In particular, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in “modular” quantum systems corresponding to quasi one-dimensional structures which consist of identical or similar many-level subunits. Such modular quantum systems are demonstrated to represent many physical situations and several examples of complex single-particle models are analyzed in detail. For these quantum systems lowest order TCL is shown to represent an efficient tool which also allows to investigate the dependence of transport on the considered length scale. To estimate the range of validity of the obtained equations of motion we extend the standard projection to include additional degrees of freedom which model non-Markovian effects of higher orders.     

The effect of local phases of wave function on transmission of a quantum particle through two dimensional clusters

We investigate the relationship between the transport properties ofordered and disordered two dimensional quantum percolation systemsand the spatial variations of the phase of the wave function. Whileoften only the spatial variations of the probability amplitudes arestudied in relation to localization and transport properties, ourstudy illustrates how crucial a role the phase variation plays. Ourinvestigation based on many different energies of the incidentparticle over the entire accessible range suggests that systems withmany neighboring sites with phase differences of ~π turn outto be those with minimal transmission, even if the probabilityamplitudes alone appear to suggest high transmission, whereas thosewith neighboring sites with ~2π, zero or small phasedifferences typically lead to high transmission. By calculatingassociated momentum distribution of the states we have shown that alow(high) transmitting state results from the equal(unequal)contribution from + and fouriercomponents. We have alsoexplored the effect of replacing diluted sites in percolation bythose with couplings that are non-zero but smaller than the onebetween undiluted sites (thus introducing finite couplinginhomogeneities instead of infinite barriers), and found that theresulting transmission can be higher or lower compared with the casewith dilution (normal, infinite barriers). Furthermore, it can behigher or lower even compared with the ordered case (uniformcouplings).     

Spin currents and magnetoresistance of graphene-based magnetic junctions

Using the tight-binding approximation and the nonequilibrium Green’s function approach, we investigate the coherent spin-dependent transport in planar magnetic junctions consisting of two ferromagnetic (FM) electrodes separated by a graphene flake (GF) with zigzag or armchair interfaces. It is found that the electron conduction strongly depends on the geometry of contact between the GF and the FM electrodes. In the case of zigzag interfaces, the junction demonstrates a spin-valve effect with high magnetoresistance (MR) ratios and shows negative differential resistance features for a single spin channel at positive gate voltage. In the case of armchair interfaces, the current-voltage characteristics behave linearly at low bias voltages and hence, both spin channels are in on state with low MR ratios.     

Shot noise in a quantum dot coupled to non-magnetic leads: effects of Coulomb interaction

We study electron transport through a quantum dot, connected to non-magnetic leads, in a magnetic field. A super-Poissonian electron noise due to the effects of both interacting localized states and dynamic channel blockade is found when the Coulomb blockade is partially lifted. This is sharp contrast to the sub-Poissonian shot noise found in the previous studies for a large bias voltage, where the Coulomb blockade is completely lifted. Moreover, we show that the super-Poissonian shot noise can be suppressed by applying an electron spin resonance (ESR) driving field. For a sufficiently strong ESR driving field strength, the super-Poissonian shot noise will change to be sub-Poissonian.     

Non-hermitian quantum mechanics in non-commutative space

A recent investigation of the possibility of having a -symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a -symmetric deformation of this space. Specifically, a -symmetric harmonic oscillator together with an iC(x ₁+x ₂) interaction are discussed in this space, and solutions are obtained. We show that in the deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative parameters. However, it is shown that in standard non-commutative space, the iC(x ₁+x ₂) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not -symmetric. A complex interacting anisotropic oscillator system also is discussed.     

Ballistic transport in bilayer nano-graphite ribbons under gate and magnetic fields

This study uses the tight-binding model to examine the ballistic transport of short and infinitely long bilayer nano-graphite ribbons for different stacked structures, AA and AB, under perpendicularly applied gate and magnetic fields. In the small bias region, the conduction of the AB-stacked ribbon is better than for the AA. Under a gate field with small bias, the AB-stacked ribbon exhibits a significant current peak at the zero gate field point, similar to the graphene ribbon. On the contrary, this current peak is not found in the AA-stacked case. Under a perpendicular magnetic field with small bias, the magnetoresistance ratio in both stacked graphene ribbons are proportional to the square of the magnetic field.     

Bound states in the continuum in two-dimensional serial structures

We investigate the occurrence of bound states in the continuum (BICs) in serial structures of quantum dots coupled to an external waveguide, when some characteristic length of the system is changed. By resorting to a multichannel scattering-matrix approach, we show that BICs do actually occur in two-dimensional serial structures, and that they are a robust effect. When a BIC is produced in a two-dot system, BICs also occur for several coupled dots. We also show that the complex dependence of the conductance upon the geometry of the multi-dot system allows for a simple picture in terms of the resonance pole motion in the multi-sheeted Riemann energy surface. Finally, we show that in correspondence to zero-width states for the open system one has a multiplet of degenerate eigenenergies for the associated closed serial system, thereby generalizing results previously obtained for single dots and two-dot structures.     

Landau analog levels for dipoles in non-commutative space and phase space

We investigate the analog of Landau quantization, for a neutral polarized particle in the presence of homogeneous electric and magnetic external fields, in the context of non-commutative quantum mechanics. This particle, possessing electric and magnetic dipole moments, interacts with the fields via the Aharonov–Casher and He–McKellar–Wilkens effects. For this model we obtain the Landau energy spectrum and the radial eigenfunctions of the non-commutative space coordinates and non-commutative phase space coordinates. Also we show that the case of non-commutative phase space can be treated as a special case of the usual non-commutative space coordinates.     

Transmission of information through mesoscopic scattering systems

The storage and transmission of information is well defined using the notions of entropy, mutual information and channel capacity as formalized by Shannon. These quantities are calculated for a quantum mesoscopic system in terms of scattering parameters. For a one-dimensional system, the mutual information is related to the thermal conductance. This relation allows to show that for an incident signal of power P, the channel capacity C has a universal upper bound given by C independent of quantum statistics. A general framework is proposed which makes use of a natural underlying symplectic structure, to relate the entropy of a quantum mesoscopic system to the scattering matrix.     

Finite correction to Aharonov-Bohm scattering by a contact potential

We study the influence of a contact (or delta) potential on the Aharonov-Bohm scattering of nonrelativistic particles. In general the contact potential has no effect on the scattering as expected. However, when the magnetic flux and the strength of the contact potential take some special values, the Aharonov-Bohm scattering cross-section is manifestly changed. It is shown that these special values correspond to the simultaneous existence of two half-bound states in two adjacent angular momentum channels. Two limiting processes are presented to deal with the singularity of the contact potential and results of the same nature are obtained.     

Dynamical method for studying localization-delocalization transition in two dimensional percolating systems

We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is determined by the disorder and interference effects, leading to interesting sharp features in conductance as the energy, disorder, and boundary conditions are varied. To aid understanding of this phenomenon, we develop a visualization method whereby the progression of a wave packet entering the cluster through a lead on one side and exiting from another lead on the other side can be tracked dynamically. Using this method, we investigate the localization-delocalization transition in a 2D system for various boundary conditions. Our results indicate the existence of two different kinds of localized regimes, namely exponential and power law localization, depending on the amount of disorder. Our study further suggests that there may be a delocalized state in the 2D quantum percolation system at very low disorder. These results are based on a finite size scaling analysis of the systems of size up to 70 × 70 (containing 4900 sites) on the square lattice.     

Quantum transport in honeycomb lattice ribbons with armchair and zigzag edges coupled to semi-infinite linear chain leads

We study quantum transport in honeycomb lattice ribbons with either armchair or zigzag edges. The ribbons are coupled to semi-infinite linear chains serving as the input and output leads and we use a tight-binding Hamiltonian with nearest-neighbor hops. The input and output leads are coupled to the ribbons through bar contacts. In narrow ribbons we find transmission gaps for both types of edges. The appearance of this gap is due to the enhanced quantum interference coming from the multiple channels in bar contacts. The center of the gap is at the middle of the band in ribbons with armchair edges. This particle-hole symmetry is because bar contacts do not mix the two sublattices of the underlying bipartite honeycomb lattice when the ribbon has armchair edges. In ribbons with zigzag edges the gap center is displaced to the right of the band center. This breakdown of particle-hole symmetry is the result of bar contacts now mixing the two sublattices. We also find transmission oscillations and resonances within the transmitting region of the band for both types of edges. Extending the length of a ribbon does not affect the width of the transmission gap, as long as the ribbon’s length is longer than a critical value when the gap can form. Increasing the width of the ribbon, however, changes the width of the gap. In ribbons with zigzag edges the gap width systematically shrinks as the width of the ribbon is increased. In ribbons with armchair edges the gap is not well-defined because of the appearance of transmission resonances. We also find only evanescent waves within the gap and both evanescent and propagating waves in the transmitting regions.     

Berry phase in open quantum systems: a quantum Langevin equation approach

The evolution of a two level system with a slowly varying Hamiltonian, modeled as a spin 1/2 in a slowly varying magnetic field, and interacting with a quantum environment, modeled as a bath of harmonic oscillators is analyzed using a quantum Langevin approach. This allows to easily obtain the dissipation time and the correction to the Berry phase in the case of an adiabatic cyclic evolution.     

Geometric phase in a composite system subjected to decoherence

In this paper, we investigate the geometric phase of a composite system which is composed of two spin- particles driven by a time-varying magnetic field. Firstly, we consider the special case that only one subsystem driven by time-varying magnetic field. Using the quantum jump approach, we calculate the geometric phase associated with the adiabatic evolution of the system subjected to decoherence. The results show that the lowest order corrections to the phase in the no-jump trajectory is only quadratic in decoherence coefficient. Then, both subsystem driven by time-varying magnetic field is considered, we show that the geometric phase is related to the exchange-interaction coefficient and polar angle of the magnetic field.     

Conductance through atomic point contacts between fcc(100) electrodes of gold

Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E_F evolves from G ≈ 3G₀ to G ≈ 1G₀ (G₀ = 2e/h²). Formation of a true one-atom point contact, with G ≈ 1G₀ and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E_F, and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range -3 ≤ E-E_F ≤ 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear “gold molecule" between the electrodes, and a weak coupling of this “molecule" to the tips.     

Geometric phase of a qubit interacting with a squeezed-thermal bath

We study the geometric phase of an open two-level quantum system under the influence of a squeezed, thermal environment for both non-dissipative as well as dissipative system-environment interactions. In the non-dissipative case, squeezing is found to have a similar influence as temperature, of suppressing geometric phase, while in the dissipative case, squeezing tends to counteract the suppressive influence of temperature in certain regimes. Thus, an interesting feature that emerges from our work is the contrast in the interplay between squeezing and thermal effects in non-dissipative and dissipative interactions. This can be useful for the practical implementation of geometric quantum information processing. By interpreting the open quantum effects as noisy channels, we make the connection between geometric phase and quantum noise processes familiar from quantum information theory.