Essential Self-Adjointness of¶Translation-Invariant Quantum Field Models¶for Arbitrary Coupling Constants

The Hamiltonian of a system of quantum particles minimally coupled to a quantum field is considered for arbitrary coupling constants. The Hamiltonian has a translation invariant part. By means of functional integral representations the existence of an invariant domain under the action of the heat semigroup generated by a self-adjoint extension of the translation invariant part is shown. With a non-perturbative approach it is proved that the Hamiltonian is essentially self-adjoint on a domain. A typical example is the Pauli–Fierz model with spin 1/2 in nonrelativistic quantum electrodynamics for arbitrary coupling constants. Received: 26 May 1999 / Accepted: 9 November 1999     

Photon counts modulation in optical time domain reflectometry

The quantum fluctuation of photon counting limits the field application of optical time domain reflection. A method of photon counts modulation optics time domain reflection with single photon detection at 1.55 μm is presented. The influence of quantum fluctuation can be effectively controlled by demodulation technology since quantum fluctuation shows a uniform distribution in the frequency domain. Combined with the changing of the integration time of the lock-in amplifier, the signal to noise ratio is significantly enhanced. Accordingly the signal to noise improvement ratio reaches 31.7 dB compared with the direct photon counting measurement.     

Self-organization of the stripe domain structure in oblique-evaporated quantum wells in vacuum

The dependence of the domain structure of oblique-evaporated quantum wells on their thickness and the angle of inclination of the easy-magnetization axis with respect to the normal to the quantum well plane has been studied. It is found that the self-organization of domain structures is mainly related to the quantum character of the cooperative phenomenon.     

Fidelity criterion for quantum-domain transmission and storage of coherent states beyond the unit-gain constraint

We generalize the experimental success criterion for quantum teleportation (memory) in continuous-variable quantum systems to be suitable for a non-unit-gain condition by considering attenuation (amplification) of the coherent-state amplitude. The new criterion can be used for a nonideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in the quantum domain.     

Visualizing the in-Gap States in Domain Boundaries of Ultra-Thin Topological Insulator Films

Ultra-thin topological insulators provide a platform for realizing many exotic phenomena such as the quantum spin Hall effect, and quantum anomalous Hall effect. These effects or states are characterized by quantized transport behavior of edge states. Experimentally, although these states have been realized in various systems,the temperature for the edge states to be the dominating channel in transport is extremely low, contrary to the fact that the bulk gap is usually in the order of a few tens of milli-electron volts. There must be other in-gap conduction channels that do not freeze out until a much lower temperature. Here we grow ultra-thin topological insulator Bi_2Te_3 and Sb_2Te_3 films by molecular beam epitaxy and investigate the structures of domain boundaries in these films. By scanning tunneling microscopy and spectroscopy we find that the domain boundaries with large rotation angles have pronounced in-gap bound states, through which one-dimensional conduction channels are suggested to form, as visualized by spatially resolved spectroscopy. Our work indicates the critical role played by domain boundaries in degrading the transport properties.     

Quantum strategies of quantum measurements

In the classical Monty Hall problem, one player can always win with probability 2/3. We generalize the problem to the quantum domain and show that a fair two-party zero-sum game can be carried out if the other player is permitted to adopt quantum measurement strategy.     

A Spatial Domain Quantum Watermarking Scheme

This paper presents a spatial domain quantum watermarking scheme. For a quantum watermarking scheme, a feasible quantum circuit is a key to achieve it. This paper gives a feasible quantum circuit for the presented scheme. In order to give the quantum circuit, a new quantum multi-control rotation gate, which can be achieved with quantum basic gates, is designed. With this quantum circuit, our scheme can arbitrarily control the embedding position of watermark images on carrier images with the aid of auxiliary qubits. Besides reversely acting the given quantum circuit, the paper gives another watermark extracting algorithm based on quantum measurements. Moreover, this paper also gives a new quantum image scrambling method and its quantum circuit. Differ from other quantum watermarking schemes, all given quantum circuits can be implemented with basic quantum gates. Moreover, the scheme is a spatial domain watermarking scheme, and is not based on any transform algorithm on quantum images. Meanwhile, it can make sure the watermark be secure even though the watermark has been found. With the given quantum circuit, this paper implements simulation experiments for the presented scheme. The experimental result shows that the scheme does well in the visual quality and the embedding capacity.     

Quantum Potential in Relativistic Dynamics

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential.     

Electron spin resonance studies on quantum tunneling in spinel ferrite nanoparticles

The electron spin resonance (ESR) spectrometer, a very sensitive instrument with fast detecting window to explore quantum phase transitions for magnetic nanoparticles, was exploited to study the fascinating interplay between thermal and quantum fluctuations in the vicinity of a quantum critical point. We have measured ESR in ferrofluid samples containing nanosize particles of Fe₂O₃. The evolution of the ESR spectrum with temperature suggests that quantum tunneling of spins occurs in single domain magnetic particles in the low temperature regime. The effects of various microwave fields, particle sizes, and temperatures on the magnetic states of single domain spinel ferrite nanoparticles are investigated. We can consistently explain experimental data assuming that, as the temperature decreases, the spectrum changes from superparamagnetic (SPR) to blocked SPR and finally evolves quantum superparamagnetic behaviour as the temperature lowers down further. A nanoparticle system of a highly anisotropic magnetic material can be qualitatively specified by a simple quantum spin model, or by the Heisenberg model with strong easy-plane anisotropy.Received: 29 August 2003, Published online: 15 October 2003PACS: 76.30.-v Electron paramagnetic resonance and relaxation - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.) - 05.30.-d Quantum statistical mechanics - 75.50.Dd Nonmetallic ferromagnetic materials     

Vortex structure in superconductors with a many-component order parameter

Abstract

The phenomenological theory of superconductors with a many-component order parameter (OP) is developed. On the basis of a generalized Ginzburg-Landau functional, equations for a two-component-OP superconductor are derived. It is shown that such a superconductor is specified by three length dimensionality parameters—penetration depth λ, correlation length ζ, and width d of the boundary between two superconducting-phase domains. With λ ? d ? ζ, the equations for the OP of a superconductor in a magnetic field can be explored analytically. The transition from the superconducting to the mixed phase may occur not only by the formation of ordinary Abrikosov vortices, but also owing to vortices that have two cores, each transferring a half-integral flux quantum. The total flux transferred by a vortex certainly constitutes an integral quantum. The cores of such a dimer are interconnected by two domain walls, which exercise confinement within the dimer. The distance between the cores in the dimer is of the order of d. Within a domain wall that separates two superconducting-phase domains, a dimer may fall apart into two vortices with a half-integral flux quantum.

For many-component-OP superconductors in a magnetic field, vortex structures of a more complicated nature than a dimer may occur. An individual core may transfer a fractional flux quantum, but the structure as a whole transfers an integral flux quantum. Confinement of individual cores occurs owing to a complicated system of domain walls determined by the topological charges of these vortices.

Under certain conditions, on attaining field H _c1, vortices may arise first in the domain walls, carrying a fractional flux quantum, and then within the superconducting domains.     

A Fredholm determinant for semiclassical quantization

We investigate a new type of approximation to quantum determinants, the "quantum Fredholm determinant," and test numerically the conjecture that for Axiom A hyperbolic flows such determinants have a larger domain of analyticity and better convergence than the Gutzwiller-Voros zeta functions derived from the Gutzwiller trace formula. The conjecture is supported by numerical investigations of the 3-disk repeller, a normal-form model of a flow, and a model 2-D map.     

Dynamics of electron in a surface quantum well

This paper studies the quantum dynamics of electrons in a surface quantum well in the time domain with autocorrelation of wave packet. The evolution of the wave packet for different manifold eigenstates with finite and infinite lifetimes is investigated analytically. It is found that the quantum coherence and evolution of the surface electronic wave packet can be controlled by the laser central energy and electric field. The results show that the finite lifetime of excited states expedites the dephasing of the coherent electronic wave packet significantly. The correspondence between classical and quantum mechanics is shown explicitly in the system.     

Synthesis and Growth Mechanism of Ultralong ZnO Nanocombs and Nanobelts on Cu Substrate

In the two-dimensional electron systems with strong coupling in MgZnO/ZnO heterostructures, the thermal behavior of Ising quantum Hall ferromagnets at the filling factor ν = 2 has been studied. The spin polarization of Hall ferromagnets has been detected by measuring the signal related to the inelastic light scattering by intrasubband spin excitons. A stepwise change in the spin polarization at the phase transition at the filling factors ν = 2,3, and 4 in the heterostructures with different electron densities has been observed. The thermal stability of the Hall ferromagnetic phases at ν = 2 has been studied and the Curie temperature has been estimated. It has been shown that the Curie temperature is determined by the formation energy for domain walls in the Ising quantum Hall ferromagnets.     

Signatures for a classical to quantum transition of a driven nonlinear nanomechanical resonator

We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental signatures, in the near future, that NEMS resonators are entering the quantum domain.     

The underlying Brownian motion of nonrelativistic quantum mechanics

Nonrelativistic quantum mechanics can be derived from real Markov diffusion processes by extending the concept of probability measure to the complex domain. This appears as the only natural way of introducing formally classical probabilistic concepts into quantum mechanics. To every quantum state there is a corresponding complex Fokker-Planck equation. The particle drift is conditioned by an auxiliary equation which is obtained through stochastic energy conservation; the logarithmic transform of this equation is the Schrödinger equation. To every quantum mechanical operator there is a stochastic process; the replacement of operators by processes leads to all the well-known results of quantum mechanics, using stochastic calculus instead of formal quantum rules. Comparison is made with the classical stochastic approaches and the Feynman path integral formulation.     

On Improving Accuracy of Finite-Element Solutions of the Effective-Mass Schrödinger Equation for Interdiffused Quantum Wells and Quantum Wires

We use the Galerkin approach and the finite-element method to numerically solve the effective-mass Schrödinger equation.The accuracy of the solution is explored as it varies with the range of the numerical domain.The model potentials are those of interdiffused semiconductor quantum wells and axially symmetric quantum wires.Also,the model of a linear harmonic oscillator is considered for comparison reasons.It is demonstrated that the absolute error of the electron ground state energy level exhibits a minimum at a certain domain range,which is thus considered to be optimal.This range is found to depend on the number of mesh nodes N approximately as α₀ log_e^α₁(α₂ N),where the values of the constants α₀,α₁,and α₂ are determined by fitting the numerical data.And the optimal range is found to be a weak function of the diffusion length.Moreover,it was demonstrated that a domain range adaptation to the optimal value leads to substantial improvement of accuracy of the solution of the Schrödinger equation.     

Stochastic interpretations of nonrelativistic quantum theory

A critique of the causla and classical stochastic interpretations of nonrelativistic quantum mechanics is presented. The only way that the classical stochastic formulation can be made compatible with the theory of quantum measurement is to extend the probability measure density for fluctuating paths to the complex domain. In doing so, we obtain the generalized stochiastic formulation in which the methods of classical probability theory can be used to describe the quantum mechanical phenomenon of interfering alternatives. Illustrative examples from quantum theory are used to show the complete compatibility between the traditional and generalized stochastic interpretations of quantum mechanics. Work supported in part by a contribution from the CNR.     

Transient properties of a bistable kinetic model with quantum corrections

The transient properties of a Brownian particle moving in a bistable system with quantum corrections are investigated. The Quantum Smoluchowski Equation (QSE) is fully valid for high temperatures; for low temperatures it is valid only in a restricted domain of the state space. The quantum effects in a bistable system stand out for low temperatures. Explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The quantum effects are against the particle moving towards the destination from its original position.     

The Origin of Structures in Generalized Gravity

In a class of generalized gravity theories with general couplings between the scalar field and the scalar curvature in the Lagrangian, we can describe the quantum generation and the classical evolution of both the scalar and tensor structures in a simple and unified manner. An accelerated expansion phase based on the generalized gravity in the early universe drives microscopic quantum fluctuations inside a causal domain to expand into macroscopic ripples in the spacetime metric on scales larger than the local horizon. Following their generation from quantum fluctuations, the ripples in the metric spend a long period outside the causal domain. During this phase their evolution is characterized by their conserved amplitudes. The evolution of these fluctuations may lead to the observed large scale structures of the universe and anisotropies in the cosmic microwave background radiation.     

Instability in superspace

Using Morse's theory of reconstructions we define the space of all the universes-the Superspace. On the Superspace we investigate the geometry of the DeWitt metric. It is shown that the geodesic flow corresponding to the DeWitt metric is exponentially instable. The dynamical system described by the Einstein equations of evolution (Einstein dynamics) has the same type of instability also, if 1) the Universe is inflationary in some local domain, 2) in some local domain the Universe does not change its volume, but changes the conformal geometry very quickly as compared with the conformal potnetial. So, the Einstein dynamics is unstable on the Superspace, therefore the following quantum theory considered on the minisuperspace (a submanifold of the Superspace with a finite dimension) says nothing about the real quantum theory on the Superspace, and in the Superspace the semiclassical approximation is close to the quantum approximation only during a short time.