Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.     

Ground state of graphene in the presence of random charged impurities

We calculate the carrier-density-dependent ground-state properties of graphene in the presence of random charged impurities in the substrate taking into account disorder and interaction effects nonperturbatively on an equal footing in a self-consistent theoretical formalism. We provide detailed quantitative results on the dependence of the disorder-induced spatially inhomogeneous two-dimensional carrier density distribution on the external gate bias, the impurity density, and the impurity location. We find that the interplay between disorder and interaction is strong, particularly at lower impurity densities. We show that, for the currently available typical graphene samples, inhomogeneity dominates graphene physics at low (< or approximately 10(12) cm(-2)) carrier density with the density fluctuations becoming larger than the average density.     

Absolute stability limit for relativistic charged spheres

We find an exact solution for the stability limit of relativistic charged spheres for the case of constant gravitational mass density and constant charge density. We argue that this provides an absolute stability limit for any relativistic charged sphere in which the gravitational mass density decreases with radius and the charge density increases with radius. We then provide a cruder absolute stability limit that applies to any charged sphere with a spherically symmetric mass and charge distribution. We give numerical results for all cases. In addition, we discuss the example of a neutral sphere surrounded by a thin, charged shell.     

Nonthermal melting of a charge density wave in TiSe2

We use time-resolved optical reflectivity and x-ray diffraction with femtosecond resolution to study the dynamics of the structural order parameter of the charge density wave phase in TiSe2. We find that the energy density required to melt the charge density wave nonthermally is substantially lower than that required for thermal suppression and is comparable to the charge density wave condensation energy. This observation, together with the fact that the structural dynamics take place on an extremely fast time scale, supports the exciton condensation mechanism for the charge density wave in TiSe2.     

The negative energy density for a three-single-electron state in the Dirac field

We examine the energy density produced by a state vector which is the superposition of three single electron states in the Dirac field in the four-dimensional Minkowski spacetime. We derive the conditions on which the energy density can be negative. We then show that the energy density satisfies two quantum inequalities in the ultrarelativistic limit.     

Simulation of Resonant Interaction between Energetic Electrons and Whistler-Mode Chorus in the Outer Radiation Belt

We construct a realistic model to evaluate the chorus wave-particle interaction in the outer radiation belt L = 4.5. This model incorporates a plasmatrough number density model, a field-aligned density model and a realistic wave power and frequency model. We solve the 2D bounce-averaged momentum-pitch-angle Fokker-Planck equation and show that the Whistler-mode chorus can be effective in the acceleration of electrons, and enhance the phase space density for energies of -1 MeV by a factor from 10 to 10^3 in about two days, consistent with the observation. We also demonstrate that ignorance of the electron number density variation along field line and magnetic local time in the previous work yields an overestimate of energetic electron phase space density by a factor 5-10 at large pitch-angle after two days, suggesting that a realistic plasma density model is very important to evaluate the evolution of energetic electrons in the outer radiation belt.     

From target to projectile and back again: self-duality of high-energy scattering evolution in QCD

We prove that the complete kernel for the high-energy evolution in QCD must be self-dual. The relevant duality transformation is formulated in precise mathematical terms and is shown to transform the charge density into the functional derivative with respect to the single-gluon scattering matrix. This transformation interchanges the high and the low density regimes. We demonstrate that the original Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner kernel, valid at large density, is indeed dual to the low density limit of the complete kernel derived recently in hep-ph/0501198.     

量子力学中的密度矩阵与具有相同密度矩阵的系综的可区分性

讨论了密度矩阵的不同定义。建议使用完全密度矩阵、压缩密度矩阵和约化密度矩阵分别描写一个封闭量子体系的、一个系综中平均分子的和一个复合体系中的一个子系统的密度矩阵。强调这与现在人们认为的具有相同压缩密度矩阵的系综是完全等价的结论完全不同,具有相同压缩密度矩阵但是成分不同的系综可以通过系综整体测量来区别。作为一个应用,现在认为现有的核磁共振量子计算中没有纠缠的结论是没有根据的。Density matrix is one important tool in quantum mechanics, and it has very broad applications. However there are different definitions about the density matrix, and they describe quite different systems. There has been some misunderstanding about the density matrix in the community, and these misunderstandings hinder the right application of the density matrix. In this article, we discuss the different definitions of density matrix. We suggest to use the full density matrix, compressed density matrix and the reduced density matrix to describe the state of a complete quantum system, the state of an averaged particle in an ensemble and the state of part of a composite system. We stress that contrary to the wide accepted understanding that ensembles with the same compressed density matrix are physically indistinguishable, they are distinguishable through the so-called ensemble measurement. As an application, we suggest that the present conclusion that the present-day nuclear magnetic resonance quantum computation does not have quantum entanglement is groundless.     

Atomic density of a harmonically trapped ideal gas near Bose-Einstein transition temperature

We have studied the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of the Bose-Einstein transition temperature. We show that, for a non-interacting gas and near this temperature, the ground-state density has the same order of magnitude as the excited states density at the centre of the trap. This holds in a range of temperatures where the ground-state population is negligible compared to the total atom number. We compare the exact calculations, available in a harmonic trap, to semi-classical approximations. We show that these latter should include the ground-state contribution to be accurate.     

Phase-space density in heavy-ion collisions revisited

We derive the phase space density of bosons from a general boson interferometry formula. We find that the phase space density is connected with the two-particle and the single-particle density distribution functions. If the boson density is large, the two-particle density distribution function cannot be expressed as a product of two single-particle density distributions. However, if the boson density is so small that the two-particle density distribution function can be expressed as a product of two single-particle density distributions, then Bertsch's formula is recovered. For a Gaussian model, the effects of multi-particles Bose-Einstein correlations on the mean phase space density are studied.Received: 10 July 2002, Revised: 18 June 2003, Published online: 5 September 2003     

No-relationship Between Impossibility of Faster-Than-Light Quantum Communication and Distinction of Ensembles with the Same Density Matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related.We argue that even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.     

No-relationship Between Impossibility of Faster-Than-Light Quantum Communication and Distinction of Ensembles with the Same Density Matrix

It has been claimed in the literature that impossibility of faster-than-light quantum communication has an origin of indistinguishability of ensembles with the same density matrix. We show that the two concepts are not related. We argue that even with an ideal single-atom-precision measurement, it is generally impossible to produce two ensembles with exactly the same density matrix; or to produce ensembles with the same density matrix, classical communication is necessary. Hence the impossibility of faster-than-light communication does not imply the indistinguishability of ensembles with the same density matrix.     

Time-dependent density functional theory of classical fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.     

Defect induced red shift in the luminescence spectra of amorphous silicon-hydrogen films

We present luminescence spectra of amorphous silicon-hydrogen films that shift to longer wavelengths with increasing defect density. We propose that the defects increase the density of states in the gap, which decreases the “thermalization gap”, which in turn shifts the luminescence spectra to the red. We also suggest that the same mechanism is present in doped amorphous silicon films.     

Power spectrum crossover in sediments of a paleolake disturbed by volcanism

We study density fluctuations from sediments of a paleolake in central Mexico that was subjected to volcanic perturbations by means of computed tomography (CT) measurements on blocks chiselled out of mines at the lake's bed. The mine walls show laminations corresponding to the alternation of low density diatom sediments and high density volcanic ash depositions. We have previously shown that there is a range of scales where these fluctuations present a self-similar behavior [1]. Here we relate density correlation calculations to the power spectrum of the fluctuations. We show that a scaling region in the power spectrum coincides with the scaling region in the correlations produced by relaxation from intense volcanic perturbations to steady state fluctuations. There appears to be a kink-like crossover in the power spectrum from mid range scaling to a shorter range scale invariance. This, together with the density probability distribution of the fluctuations, draws attention to the dominant role of rare events. We believe that our analysis may be useful for the understanding of other phenomena with similar power spectrum properties, in which a scale invariance in the unperturbed system is altered by external perturbations that induce an additional scaling behavior.     

Unexpected negative nonmonotonic magnetoresistance of the two-dimensional electrons in Si in a parallel magnetic field

We report observation of the unexpected negative and nonmonotonic magnetoresistance of 2D electrons in Si-MOSFET subjected to a varying in-plane magnetic field superimposed on a constant perpendicular field component. We show that this nonmonotonic magnetoresistance is irrelevant to the energy spectrum of mobile 2D electrons. We also observed variations of the density of mobile electrons with the in-plane field. We argue that both variations of the negative magnetoresistance and of the density of mobile electrons originate from the band of localized states. The latter coexist and interact with mobile electrons even at relatively high density, a factor of 1.5 higher than the critical density of the apparent metal-insulator transition.     

Spectral density of mixtures of random density matrices for qubits

We derive the spectral density of the equiprobable mixture of two random density matrices of a two-level quantum system. We also work out the spectral density of mixture under the so-called quantum addition rule. We use the spectral densities to calculate the average entropy of mixtures of random density matrices, and show that the average entropy of the arithmetic-mean-state of n qubit density matrices randomly chosen from the Hilbert–Schmidt ensemble is never decreasing with the number n. We also get the exact value of the average squared fidelity. Some conjectures and open problems related to von Neumann entropy are also proposed.     

The ideal Boson gas in an external scalar potential

We consider a new way of going to the infinite volume thermodynamic limit for a finite density quantum system and apply it to the case of an ideal Boson gas. We describe two procedures for calculating the particle density in the thermodynamic limit, one local and one global, and show that they give different values for the density. Further calculations show that this discrepancy is caused by lack of macroscopic translation invariance of the system, which is not apparent at the microscopic level. We calculate the limiting value of the expectation function of the Weyl operators both above and below the critical density for Bose-Einstein condensation, and show that the condensate has paradoxical properties of a similar type to those recently discovered for the rotating Boson gas.     

Instability in a network coevolving with a particle system

We study the coupled dynamics of a network and a particle system. Particles of density rho diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics leads to an instability toward the formation of hubs and that there is a dynamic phase transition at a threshold particle density rho c. In the low density phase, the network evolves into a star-shaped one with the maximum degree growing linearly in time. In the high density phase, the network exhibits a fat-tailed degree distribution and an interesting dynamic scaling behavior. We present an analytic theory explaining the mechanism for the instability and a scaling theory for the dynamic scaling behavior.     

Fluid-dynamical description of the gap fluctuations of two trapped fermion species

We apply a recent generalisation of the fluid-dynamical scheme developed for two trapped fermion species with pairing interactions to examine the fluctuations of the gap density coupled to the particle transition density at low energy. The dynamical scheme satisfies Kohn’s theorem for both the particle density and the pairing gap. We analyse the form of the gap fluctuations in a spherical trap in terms of their multipolarity and the interaction strength, and find that coupling to the particle density produces considerable stiffness of the gap transition density together with compression towards the centre of the trap.