Hilbert-Schmidt distance and non-classicality of states in quantum optics

Abstract

The Hilbert—Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states. Unitary transformations of both states with the same unitary operator (e.g. the displacement of both states in the phase plane by the same displacement vector and squeezing of both states) do not change this distance. The nearest distance of a given state to the whole set of coherent states is proposed as a quantitative measure of non-classicality of the state which is identical when considering the coherent states as the most classical ones among pure states and the deviations from them as non-classicality. The connection to other definitions of the non-classicality of states is discussed. The notion of distance can also be used for the definition of a neighbourhood of considered states. Inequalities for the distance of states to Fock states are derived. For given neighbourhoods, they restrict common characteristics of the state as the dispersion of the number operator and the squared deviation of the mean values of the number operator for the considered state and the Fock state. Possible modifications in the definition of non-classicality for mixed states with dependence on the impurity parameter and by including the displaced thermal states as the most classical reference states are discussed.     

Phase-sensitive non-classicality criteria for phase-independent quantum states

A recently introduced hierarchy of necessary and sufficient conditions for non-classicality of a quantum state [Th. Richter and W. Vogel, Phys. Rev. Lett. 89 283601 (2002)] is applied to the characterization of phase-insensitive quantum states. Even under such conditions it may be important to analyse the relation between different phase values in the quadrature distributions in order to demonstrate the non-classical nature of the state under study.     

Mathematical models for the numerical study of turbulent flows

Abstract

This paper presents (1) a brief overview of the mathematical models used in the numerical study of turbulent flows; (2) a K‐? model of turbulence; and (3) extensions of the K‐? model to account for some of the effects of compressibility, low Reynolds number, streamline curvature, and preferential stress dissipation.     

Quantum coherence of optical systems and dissipation

Abstract

We show that in an open optical system with one-photon dissipation formation of a stationary even coherent superposition state is possible, which is a consequence of the fact that the lifetime of the optical system in a coherent superposition state is different for even and odd states.     

Rate of energy dissipation of the thermal fluctuation field of the sample at the tip of a tunneling microscope

It is shown that the rate of energy dissipation of the thermal field of a sample at the tip of a microscope is inversely proportional to the cube of the distance between tip and sample. Pis’ma Zh. Tekh. Fiz. 23, 49–53 (February 12, 1997)     

Squeezed-state Superpositions in a Damped Nonlinear Oscillator

Abstract

The effect of dissipation on squeezed-state superposition states, generated in a nonlinear oscillator is investigated. Our results are presented in terms of the Q-function and the marginal distributions for a class of Hermitian operators.     

A simulation study on the effect of spring-shaped fillers on the viscoelasticity of rubber nanocomposite

Background/PurposeRubber nanocomposites have been widely used in many engineering fields due to their unique properties such as high elasticity and viscoelasticity. Much attention has been paid to the viscoelasticity of rubbers because it directly relates to the performance of the rubber products.MethodsBased on the micromechanical theory, the finite element method is used to analyze the effect of elastic modulus and volume content of spring-shape nanofillers on the dynamic viscosity of composites.ResultsThe simulation results show that there is an optimal elastic modulus of spring-shape nanofillers to make the loss factor a minimum. There is a threshold value of spring-shape nanofiller content for the dissipation energy density of composite.ConclusionThe elastic modulus of spring-shape nanofillers has a large effect on the loss factor of composites. The selection of elastic modulus of spring-shape nanofillers is critical for applications of composites. The efficiency of spring-shape nanofillers in reducing the dynamic viscosity of composites is so high that volume content of spring-shape nanofillers as low as 0.1% can greatly reduce the loss factor of composites with bonding interface.     

A DRBEM model for harbor oscillation with the effect of energy dissipation

Abstract

In this study, the numerical scheme of dual reciprocity boundary element method (DRBEM) is adopted to investigate the resonant problem in a harbor while considering the effect of energy dissipation. The numerical model employed the mild slope equation as a basic equation. To avoid complicated procedures for solving the equation, DRBEM is used to improve numerical efficiency. Computation results are compared with the existing experimental data and other theoretical results. It shows that the present model is valid and effective to solve the harbor oscillation problem.     

Bloch equations and completely positive maps

Abstract

The phenomenological dissipation of the Bloch equations is re-examined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and coloured stochastic noise.     

BER evaluations for multimode beams in underwater turbulence

Abstract

In underwater optical communication links, bit error rate (BER) is an important performance criterion. For this purpose, the effects of oceanic turbulence on multimode laser beam incidences are studied and compared in terms of average BER (<BER>), which is related to the scintillation index. Based on the log-normal distribution, <BER> is analysed for underwater turbulence parameters, including the rate of dissipation of the mean squared temperature, the rate of dissipation of the turbulent kinetic energy, the parameter that determines the relative strength of temperature and salinity in driving index fluctuations, the Kolmogorov microscale length and other link parameters such as link length, wavelength and laser source size. It is shown that use of multimode improves the system performance of optical wireless communication systems operating in an underwater medium. For all the investigated multimode beams, decreasing link length, source size, the relative strength of temperature and salinity in driving the index fluctuations, the rate of dissipation of the mean squared temperature and Kolmogorov microscale length improve the <BER>. Moreover, lower <BER> values are obtained for the increasing wavelength of operation and the rate of dissipation of the turbulent kinetic energy in underwater turbulence.     

Comparison Between the Characters of the Influence of Nonlinear Dispersion and Intrapulse Raman Scattering on Stationary Waves

Abstract

The action of the nonlinear dispersion and intrapulse Raman scattering on the stationary waves is investigated. The existence of the stationary periodical waves is predicted in the case of the presence of nonlinear dispersion. The action of intrapulse Raman scattering is quite different; it operates as a nonlinear force of dissipation which destroys stationary waves.     

Propagation characteristics of plane waves of defects in a viscoplastic medium

It is shown that dispersion is not observed in the propagation of a weakly damped wave, and dissipation is frequency-dependent. For strongly damped waves, dispersion and dissipation are observed. However, a wave in a viscoplastic medium decays over very short distances and the penetration depth of strongly damped waves of defects is bounded by the skinlayer thickness. Pis’ma Zh. Tekh. Fiz. 25, 91–94 (September 26, 1999)     

Solution of low péclet number heat transfer with viscous dissipation in the semi‐infinite axial region of a tube via functional analytic methods

Abstract

A solution of the extended Graetz problem with prescribed wall heat flux and viscous dissipation in a semi‐infinite axial region of a tube is obtained by functional analytic methods. The energy equation is split into a set of partial differential equations to obtain a self‐adjoint formulism. Then, an algebraic characteristic equation of the eigenvalue problem for an arbitrary velocity profile is obtained by an approximation method in L ₂[0, 1]. In addition, a backward recursive formula for calculating the expansion coefficients of the solution is developed.     

Time evolution of entanglement and bistability of two coupled quantum dots in a driven cavity

Abstract

The time evolution of entanglement between two quantum dots (QDs) trapped inside a cavity driven by a coherent quantized field is studied. In the presence of dissipation, entanglement shows many interesting features such as sudden death and revival, and finite steady state value after sudden death. We also investigate dependence of entanglement on dot variables and its relation to bistability. It is found that entanglement vanishes when the cavity field intensity approaches the upper branch of the bistability curve. When the cavity is driven by a modulated field in the presence of dissipation, it can periodically generate entanglement, which is much larger than the maximum value attained in the steady-state for this system but the dots are never fully entangled.     

Soliton propagation in nonlinear optics with higher-order effects

Abstract

We consider the nonlinear wave propagation in a single-mode dielectric waveguide. Considering the envelope equation by Kodama and Hasegawa, which consists of the higher-order terms in the form of higher-order dispersion and dissipation, we investigate the conditions for which the system admits soliton-type pulse propagation through Painlevé analysis. We also present N-soliton solutions.     

Nonlinear Dissipative Oscillator with Displaced Number States

Abstract

We study the interaction of a Kerr-like medium with light initially prepared in a displaced number state. We analyse squeezing properties and photon statistics at the output of a Kerr-like medium. We show that under certain conditions the superposition of two displaced number states can be created. We study the influence of dissipation on the formation of the superposition state.     

Photodeflection response of a gyrotropic-isotropic sample under conditions of tunneling electromagnetic interference

Calculations of the energy dissipation of oppositely directed light beams in a gyrotropic-isotropic sample are used to determine the photodeflection response. It is shown that the photodeflection signal can be completely suppressed when the beams interact while propagating in opposite directions. Pis’ma Zh. Tekh. Fiz. 24, 85–89 (August 12, 1998)     

Processing parameters for the mechanical working of 9 Cr–1 Mo steel: processing maps approach

Abstract

Processing and instability maps using a dynamic materials model have been developed for 9Cr–1Mo steel in the temperature range 850 to 1200°C and strain rate range 0.001–100 s^–1 with a view to optimising its hot workability. The efficiency of power dissipation increased with increase in temperature and decrease in strain rate. The 9Cr–1Mo material exhibited two dynamic recrystallisation domains, one with a peak efficiency of 37% occurring at 950°C and 0.001 s^–1 and the other with a peak efficiency of 35% occurring at 1200°C and 0.1 s^–1. These results are in good agreement with those found in industry.     

Design of an adjustable‐way cache for energy reduction

Abstract

Conventional set‐associative caches, with higher associativity, provide lower miss rates. However, they suffer from longer hit access time and larger energy dissipation. Based on the consideration of different program localities, programs should have their own appropriate associativity of caches. In this paper, we propose a set‐associative cache that can provide flexibilities to adjust its associativity according to different program behaviors, which means that the proposed cache scheme can be adjusted from an n‐way set‐associative cache to a direct‐mapped cache. By use of this cache architecture, power consumption can be lowered when an n‐way set‐associative cache configures the cache with lower associativity (less than n) due to only enabling fewer subarrays of the tag memory and data memory. However, the performance is still maintained at the same level as in a conventional set‐associative cache or direct‐mapped cache. Adjustable‐way set‐associative caches can also be applied to multiprocessor systems to reduce the average, overall system, energy dissipation.