The resolvent algebra: A new approach to canonical quantum systems

The standard C^∗-algebraic version of the algebra of canonical commutation relations, the Weyl algebra, frequently causes difficulties in applications since it neither admits the formulation of physically interesting dynamical laws nor does it incorporate pertinent physical observables such as (bounded functions of) the Hamiltonian. Here a novel C^∗-algebra of the canonical commutation relations is presented which does not suffer from such problems. It is based on the resolvents of the canonical operators and their algebraic relations. The resulting C^∗-algebra, the resolvent algebra, is shown to have many desirable analytic properties and the regularity structure of its representations is surprisingly simple. Moreover, the resolvent algebra is a convenient framework for applications to interacting and to constrained quantum systems, as we demonstrate by several examples.     

Multi-spin-subband structure of dilute magnetic semiconductor quantum wells: Feedback mechanism

Using a fully self-consistent envelope function approach, we focus on wide conduction band NMS (non-magnetic semiconductor)/DMS (dilute magnetic semiconductor)/NMS quantum wells, under weak external parallel magnetic field, where many spin-subbands are usually present. We concentrate on small values of the magnetic field because we want to investigate the influence of the feedback mechanism due to the difference of the concentrations of spin-up and spin-down carriers which could induce spontaneous spin-polarization i.e. in the absence of a magnetic field. We study the spin-subband structure, the spin-subband populations and the spin-polarization as functions of the sheet carrier concentration, _Ns$N_s$, for different values of the magnitude of the exchange interaction, |J|$\left|J\right|$, between the itinerant carriers and the magnetic impurities. Our calculations for 0.01 T show that at 20 K the values of |J|$\left|J\right|$ necessary to make this feedback mechanism sufficiently strong are too high compared to the |J|$\left|J\right|$ values of common Mn-doped systems in the conduction band. However, the feedback mechanism will be sufficiently strong at low enough temperatures below 20 K for realistic values of |J|$\left|J\right|$. Moreover, we explain how increasing the sheet carrier concentration the heterostructure is transformed from an almost square quantum well to a system of two coupled heterojunctions with an intermediate soft barrier.     

Diffusive corrections to asymptotics of a strong-field quantum transport equation

The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number ?, evolution equations are derived for the terms of zeroth and first order in ?. In particular, a quantum drift-diffusion equation for the position density of electrons, with an ?-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order ?², uniformly in time and for arbitrary initial data is given.     

Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.     

Spin current pumping with two orthogonal electric fields in quantum wire

We study the problem of spin current pumping in a one-dimensional quantum wire when there exist two orthogonal Rashba spin-orbit couplings (SOCs) in different regions which evolve with time and can be induced by the perpendicular electric fields. On one hand, we demonstrate that the time-evolving Rashba SOC is equivalent to the spin-dependent electric field and the scheme may lead to the pure spin current associated with well suppressed charge current. On the other hand, we adopt the non-equilibrium Green's function method and numerically find that the parameter loop must satisfy certain condition for the successful pumping. We also study the effect of the Fermi energy and the inevitable disorder on the spin current. The implications of these results are discussed.     

Well-crystallized zinc oxide quantum dots with narrow size distribution

In this study, pulsed laser ablation, online annealing, and following size classification using a differential mobility analyzer (DMA) were employed to fabricate quantum dots (QDs) of zinc oxide (ZnO). The irregularly shaped ZnO particles were obtained at annealing temperature less than 873 K, which gradually transformed into spherical QDs with increasing the annealing temperature. Finally, ZnO QDs with narrow size distribution having spherical shapes were successfully obtained at temperatures above 1173 K under the DMA classification at a nominal size of 10 nm. TEM observation demonstrated that the ZnO QDs obtained by this process were well-crystallized single crystallites with a wurtzite structure. Further, ZnO QDs with average sizes in the range of 4.8–8.1 nm were successfully fabricated by reducing the specified sizes of DMA. These features of the fabricated ZnO QDs are favorable for investigation of intrinsic quantum size effect in ZnO.     

The Ensemble Quantum State of a Single Particle

The derivation of the statistical nature of the quantum mechanical wave function is presented within the formalism of quantum mechanics and the second quantization. The statistical wave function may be derived for non relativistic bosons, non relativistic fermions, and relativistic bosons by employing the commuting field operator . For relativistic electrons a strictly anticommuting must be employed to derive the statistical wave function (spinor). The discussion at the end of the paper aims to show the physical plausibility of a statistical wave function.     

A hydrodynamic approach to multidimensional dissipation-based Schrödinger models from quantum Fokker-Planck dynamics

In this paper we are concerned with the modeling of quantum dissipation and diffusion effects at the level of the multidimensional Schrödinger equation. Our starting point is the quantum Fokker-Planck master equation describing dissipative interactions (of mass and energy) of the particle ensemble with a thermal bath in thermodynamic equilibrium. When considering its associated hydrodynamic system, which rules the temporal evolution of the local density and the mean fluid-flow velocity, and imposing physically admissible closure relations, these equations can be seen as describing the fluid-mechanical evolution of the macroscopic amplitude and phase of an envelope wavefunction, thus giving rise to a family of dissipative Schrödinger equations of logarithmic type whose steady state and radial dynamics are analyzed. Also, numerical comparison with the exactly solvable models for the free particle and the damped harmonic oscillator is performed.     

Discreteness of space from GUP II: Relativistic wave equations

Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrödinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one-dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this Letter, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected Klein–Gordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.     

Synthesis of quantum-confined CdS nanotubes

CdS nanotubes with wall thickness comparable to excitonic diameter of the bulk material are synthesized by a chemical route. A change in experimental conditions result in formation of nanowires, and well-separated nanoparticles. The diameter and wall thickness of nanotubes measured to be 14.4 ±  6.1 and 4.7 ± 2.2 nm, respectively. A large number of CdS nanocrystallites having wurzite structure constitute these nanotubes. These nanotubes show high energy shifting of optical absorption and photoluminescence peak positions, compared to its bulk value, due to quantum confinement effect. It is proposed that nucleation and growth of bubbles and particles in the chemical reaction, and their kinetics and interactions are responsible for the formation of nanotubes.