Hund’s rule in the two-electron quantum dot

Hund??s rule, specifying that in an open shell configuration the state of higher total spin has a lower energy, is also applicable to few-electron quantum dots. However, the relative contributions of the different energetic components behave in a qualitatively distinct way. This is accounted for by application of the virial theorem.     

Haag’s theorem in noncommutative quantum field theory

Haag’s theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.     

On the relation of Manin’s quantum plane and quantum Clifford algebras

In a recent work we have shown that quantum Clifford algebras — i.e. Clifford algebras of an arbitrary bilinear form — are closely related to the deformed structures asq-spin groups, Hecke algebras,q-Young operators and deformed tensor products. The question to relate Manin’s approach to quantum Clifford algebras is addressed here. Explicit computations using the CLIFFORD Maple package are exhibited. The meaning of non-commutative geometry is reexamined and interpreted in Clifford algebraic terms. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Molecular ordering in a bipolar nematogenic cyanobiphenyl – a computer simulation approach

The molecular ordering of 4-(6-hydroxypropyloxy)-4′-cyanobiphenyl (H3CBP), a bipolar nematogen, has been carried out at room temperature (300 K) with respect to translatory and orientational motions. The complete neglect differential overlap (CNDO/2) method has been employed to compute the net atomic charge and atomic dipole moment at each atomic center. The modified Rayleigh–Schrodinger perturbation theory with multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a 6-exp potential function has been assumed for short-range interactions. The interaction energy values obtained through these computations were used to calculate the probability of each configuration at room temperature using the Maxwell–Boltzmann formula. On the basis of stacking, in-plane, and terminal interactions energy calculations, all possible geometrical arrangements of the molecular pair have been considered. Further, an attempt has been made to develop a model for liquid crystallinity based on probability of dimer complexes.     

Macroscopic simulation of violation of Bell’s inequality

A macroscopic quantum model of a two-level system (the analogue of a half-spin particle) is described. The model is employed for simulating not only the system under study, but the measurement process as well. Single- and two-particle state models of a quantum system are constructed. The Einstein-Podolsky-Rosen paradox and Bell’s inequality are discussed within the framework of the model.     

Exact analytic relation between quantum defects and scattering phases with applications to Green’s functions in quantum defect theory

The relation between the quantum defects, , and scattering phases, , in the single-channel Quantum Defect Theory (QDT) is discussed with an emphasis on their analyticity properties for both integer and noninteger values of the orbital angular momentum parameter . To derive an accurate relation between and for asymptotically-Coulomb potentials, the QDT is formally developed for the Whittaker equation in its general form “perturbed” by an additional short-range potential. The derived relations demonstrate that is a complex function for above-threshold energies, which is analogous to the fact that is complex for below-threshold energies. The QDT Green's function, , of the “perturbed” Whittaker equation is parameterized by the functions and for the continuous and discrete spectrum domains respectively, and a number of representations for are presented for the general case of noninteger . Our derivations and analyses provide a more general justification of known results for nonrelativistic and relativistic cases involving Coulomb potentials and for a Coulomb plus point dipole potential. Received 25 June 1999     

Temperature dependence of violation of Bell’s inequality in coupled quantum dots in a microcavity

Bell’s inequality in two coupled quantum dots within cavity QED, including Förster and exciton–phonon interactions, is investigated theoretically. It is shown that the environmental temperature has a significant impact on Bell’s inequality.     

Opening the Pandora’s box of quantum spinor fields

Lounesto’s classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.     

‘Monte Carlo’ computer simulation of chain molecules III. Simulation of n-alkane molecules

Considering a realistic model for isolated n-alkane molecules, their configurational behaviour has been explored employing a ‘Monte Carlo’ method. The present study shows that the behaviour of the short molecules is unlike that of the longer molecules in regard to the variation with temperature of the mean-square end-to-end distance and radius of gyration. For the short molecules the mean-square end-to-end distance and the radius of gyration are decreasing functions of temperature, but they increase with temperature in the case of the longer molecules. The macromolecules assume random-walk behaviour at approximately 600 K. The computed heat capacity versus temperature curves disclose configurational transitions in the chains.     

Eavesdropping on the＇ping-pong＇ quantum communication protocol freely in a noise channel

We introduce an attack scheme for eavesdropping freely the ping-pong quantum communication protocol proposed by Bostr\"{o} m and Felbinger [Phys. Rev. Lett. 89, 187902 (2002)] in a noise channel. The vicious eavesdropper, Eve, intercepts and measures the travel photon transmitted between the sender and the receiver. Then she replaces the quantum signal with a multi-photon signal in the same state, and measures the returned photons with the measuring basis, with which Eve prepares the fake signal except for one photon. This attack increases neither the quantum channel losses nor the error rate in the sampling instances for eavesdropping check. It works for eavesdropping the secret message transmitted with the ping-pong protocol. Finally, we propose a way for improving the security of the ping-pong protocol.     

Information leak in Liu et al.’s quantum private comparison and a new protocol

In a recent paper [W. Liu, Y.B. Wang, Z.T. Jiang, Opt. Commun. 284, 3160 (2011)], a quantum private comparison (QPC) protocol based on W states was presented. Compared to the previous QPCs, the protocol is promising for that it can prevent the comparison result from revealing to the third party. However, this study point out that a flaw of information leak is existent in the protocol. And a new QPC which can avoid the flaw and has higher efficiency is proposed in this paper.     

Green’s functions and strength functions for stationary quantum systems

By using the analytic properties of the retarded Green’s function for a stationary quantum system, the strength function that coincides with the energy distribution of an unperturbed state of the system over its exact states in a perturbing field is constructed. It is shown that, in general, this strength function has the form of a Breit-Wigner distribution with energy-dependent parameters and that its moments are determined by the expectation values of various powers of the exact Hamiltonian for the wave function of the unperturbed state. The strength function averaged over a certain energy interval is calculated, and its properties are investigated for a global regime of averaging. The resulting strength functions are used to determine the mean field and the optical potential for nucleons in nuclei and to investigate conditions under which quantum chaos emerges in various systems.     

Quantum transport of spin-polarized carriers in quasi paramagnetic quantum wires: Green’s function formalism

In this paper, the Schrödinger equation is solved for approximation of the ground state energies and associated wave functions of carriers confined in a rectangular semiconductor (SC) quantum wire embedded in a SiO₂ matrix. The problem was treated with the effective one band Hamiltonian. The finite difference scheme was used for the discretization of 2D Schrödinger equation and LAPACK package to resolve the band matrix. The energy levels were determined and the coupling between quantum wires was investigated. The effect on energies and relative wave functions of quantum wires number, size and separation was studied. The results obtained show that the energy levels can be importantly modified and controlled by these parameters. The interaction is manifested by a reduction in energies and an increase in the peak value of the wave function of the higher energy wire. This study offers a fast and inexpensive way to check device designs and processes and can be used in diverse device applications.     

The topological quantum field theory of Riemann’s theta functions

In this paper we prove the existence and uniqueness of a topological quantum field theory that incorporates, for all Riemann surfaces, the corresponding spaces of theta functions and the actions of the Heisenberg groups and modular groups on them.     

The Green’s function in a channel with a sound-absorbing cover in the case of a uniform flow

We study the modal structure of an acoustic field of a point source as function of channel wall admittance in the case of a two-dimensional channel. The characteristic equation for determining the eigen-values corresponding to the boundary problem is studied in the form of this equation??s dependence on the admittance, which varies in the entire complex plane. All modes, without exception, existing in the channel and forming the source field are classified based on the obtained topography of the characteristic equation. The expressions that describe the amplitudes and spatial distribution of the hydrodynamic modes, attenuation rate (for stable modes), or increment (for unstable modes) were obtained as functions of the wall admittance and flow velocity. It is shown that in addition to the hydrodynamic unstable modes existing downstream from the source, hydrodynamic unstable modes exist upstream from the source at any admittance. They appear only when the admittance has an elastic character. It is shown that hydrodynamic modes are induced only in the case when the source is located close to the wall or on the wall. The amplitude of these modes decreases exponentially with distance from the wall.     

IRS-assisted covert communication with eavesdropper’s channel and noise information uncertainties

This paper considers an intelligent reflecting surface (IRS)-assisted covert communication system, where an IRS is deployed for the covert transmission from a legitimate transmitter (Alice) to a legitimate receiver (Bob) with the presence of an eavesdropper (Willie). Since Willie is not a legitimate communication node and cannot control the IRS’s reflection, it has uncertainty about the channel information of the Alice-IRS and IRS-Willie links. Meanwhile, Willie also has uncertainty about its noise power. Having such channel and noise information uncertainties, Willie finds an optimal power detection threshold to minimize its false detection probability. Under this system setup, we investigate maximizing the covert rate of the legitimate communication from Alice to Bob, by jointly optimizing Alice’s transmit power and the IRS’s reflecting phase shifts. We have proposed two efficient joint optimization algorithms for the continuous and discrete IRS reflecting phase shift cases, respectively. The proposed algorithm for the previous case is based on the semidefinite relaxation technique, and that for the latter case is based on the alternating optimization technique. Simulation results have demonstrated the superiority and necessity of jointly optimizing the transmit power and IRS reflecting phase shifts on improving the covert rate performance, as compared to other benchmark schemes.     

Efficient β-formulation for the FEM analysis of leaky modes in general anisotropic channel waveguides

An efficient method to model guided and leaky modes of anisotropic dielectric waveguides with arbitratry dielectric tensor ¯¯ is presented. This method takes advantage of a particular -formulation approach of the finite element method (FEM), leading to an optimized use of the computational resources.     

On the possibility of implementation of Kohn’s theorem in the case of ellipsoidal quantum dots

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional, coupled. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the dot in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system.     

Probability distribution and Bell’s inequality for the quantum qubit state

The problem of Bell’s inequality violation for a particle with spin 1/2 is studied within the tomographic approach. Two possible methods for constructing the distribution functions associated with the qubit quantum state are presented. The Bell parameter maximum is studied for each proposed distribution.