Classical and path-integral molecular-dynamics study on liquid water and ice melting using non-empirical TTM2.1-F model

The TTMF2.1-F model is a non-empirical intermolecular water potential parametrised from ab-initio calculations of the water dimer with a complete basis set limit including dispersion correction from second-order Moller-Plesset perturbation theory. In this work, using two-phase ice-water NVT molecular-dynamics (MD) simulations, we found the ice melting temperature using the TTM2.1-F potential is close to 273?K when the nuclear quantum effects (NQEs) were included using path-integral centroid MD. Detailed analysis of the radial distribution functions, angle distribution functions, and associated joint probability for both liquid water and the two-phase cases showed that the melting-point-temperature drop when using path-integral simulation is due to the weakening of hydrogen bonds vis-à-vis classically-propagated MD.     

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects (superconducting granules, superfluid helium in a porous medium, traps with Bose-condensed atoms, etc.) is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number n ₀ of the sites in the system (the “number of Cooper pairs” per granule, the number of atoms in a trap, etc.) leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on n ₀. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in n ₀ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum path-integral Monte Carlo calculations. Zh. éksp. Teor. Fiz. 114, 591–604 (August 1998)     

The compressibility theorem for quantum simple fluids at equilibrium

An extension of the compressibility theorem for quantum simple fluids within the pathintegral approach is presented. First, it is demonstrated that in the absence of quantum exchange, the isothermal compressibility can be formulated in an exact manner with the use of the pair radial correlation function of the path-integral centroids corresponding to the particles of the fluid. This adds up to the two known formulations based on the pair correlations between true quantum particles, namely the instantaneous and the pair linear response correlations. To complement this extension, an exact Ornstein-Zernike equation for pair centroid correlations is derived, which permits accurate estimates for the isothermal compressibility to be obtained. Several fluids are studied, new numerical results for the latter quantity are reported to support the theoretical points, and some difficulties present in this sort of calculation are discussed. The systems studied are the following: the quantum hard sphere fluid with and without attractive Yukawa interaction, liquid helium-4 and liquid para-hydrogen. Finally, the possibilities of extending the theorem to deal with quantum exchange are considered, and it is shown that the extension and its computational Ornstein-Zernike scheme also hold for a Bose fluid.     

A Discrete, Deterministic Construction of the Phase in Feynman Paths

In the path-integral formulation of quantum mechanics, the phase factor e ^iS(x〈t〉) is associated with every path x〈t〉. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the complex phase was a mathematical device invoked to extract wave behaviour in a particle framework. In this paper we show that the continuous phase itself can have a discrete origin in time reversal and that the propagator can be drawn by a single deterministic path. ¹On leave from Department of Mathematics, Ryerson University, Toronto, Ontario Canada.     

Diagrammar in classical scalar field theory

In this paper we analyze perturbatively a g?⁴classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost “identical” formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

A unified quantum theory of mechanics and thermodynamics. Part IIb. Stable equilibrium states

Part IIb presents some of the most important theorems for stable equilibrium states that can be deduced from the four postulates of the unified theory presented in Part I. It is shown for the first time that the canonical and grand canonical distributions are the only distributions that are stable. Moreover, it is shown that reversible adiabatic processes exist which cannot be described by the dynamical equation of quantum mechanics. A number of conditions are discussed that must be satisfied by the general equation of motion which is yet to be discovered.Part I of this paper appeared inFound. Phys. 6(1), 15 (1976). Part IIa appeared inFound. Phys. 6(2), 127 (1976). The numbering of the sections, equations, and references in this part of the paper continues from those in Part IIa.     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

Interpolating gauges and the importance of a careful treatment of ε-term

We consider the use of interpolating gauges (with a gauge function F[A;]) in gauge theories to connect the results in a set of different gauges in the path-integral formulation. We point out that the results for physical observables are very sensitive to the epsilon term that we have to add to deal with singularities and thus it cannot be left out of a discussion of gauge-independence generally. We further point out, with reasons, that the fact that we can ignore this term in the discussion of gauge independence while varying of the gauge parameter in Lorentz-type covariant gauges is an exception rather than a rule. We show that generally preserving gauge-independence as is varied requires that the -term has to be varied with . We further show that if we make a naive use of the (fixed) epsilon term (that is appropriate for the Feynman gauge) for general interpolating gauges with arbitrary parameter values [i.e. ], we cannot preserve gauge independence [except when we happen to be in the infinitesimal neighborhood of the Lorentz-type gauges]. We show with an explicit example that for such a naive use of an -term, we develop serious pathological behavior in the path-integral as is/are varied. We point out that correct way to fix the -term in a path-integral in a non-Lorentz gauge is by connecting the path-integral to the Lorentz-gauge path-integral with correct -term as has been done using the finite field-dependent BRS transformations in recent years.     

On locality in quantum general relativity and quantum gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.     

An efficient deterministic secure quantum communication scheme based on cluster states and identity authentication

A novel efficient deterministic secure quantum communication scheme based on four-qubit cluster states and single-photon identity authentication is proposed. In this scheme, the two authenticated users can transmit two bits of classical information per cluster state, and its efficiency of the quantum communication is 1/3, which is approximately 1.67 times that of the previous protocol presented by Wang et al [Chin. Phys. Lett. 23 (2006) 2658]. Security analysis shows the present scheme is secure against intercept-resend attack and the impersonator's attack. Furthermore, it is more economic with present-day techniques and easily processed by a one-way quantum computer.     

A Novel Application of Probabilistic Teleportation: p-Rabin Quantum Oblivious Transfer of a Qubit

So far, all existing quantum oblivious transfer protocols focused on realization of the oblivious transfer of a classical bit or classical bit-string. In this paper, p-Rabin quantum oblivious transfer of a qubit protocol is achieved by using a probabilistic teleportation protocol. As the probabilistic teleportation protocol is able to transfer an (un)known pure state with a certain probability, this feature makes the probabilistic teleportation protocol well fit for Rabin oblivious transfer. Here, this is the first time that the concept of qubit oblivious transfer is presented. Furthermore, p-Rabin quantum oblivious transfer of a qubit protocol can also be used for oblivious of a bit by encoding classical bit with two pre-agreed orthogonal states. Finally, security analysis shows that the protocol satisfies the security requirements of oblivious transfer, and what’s more, the discussion of relationship with no-go theorem demonstrates that the probabilistic teleportation protocol is able to evade the no-go theorem.

     

Modeling Modal Talk in Quantum Mechanics

In this paper, modal and counterfactual logical connectives are defined in an extended framework of branching space-time (Belnap, N. D. (1992). Branching space-time. Synthese 92, 385–434). It is shown that a variety of definitions of the counterfactual can be given. The validity of certain modal statements occurring in quantum mechanics depends on the choice of definition. These considerations can be applied to an analysis of Stapp’s premises LOC1 and LOC2 from his purported proof of non-locality (Stapp, H. P. (1997). Nonlocal character of quantum theory. American Journal of Physics 65, 300–304). It is shown that while the validity of LOC1 depends on the choice of the definition of the counterfactual, LOC2 is absolutely invalid.     

Path integral for Koenigs spaces

I discuss a path-integral approach for the quantum motion on two-dimensional spaces according to Koenigs, for short “Koenigs spaces”. Their construction is simple: one takes a Hamiltonian from a two-dimensional flat space and divides it by a two-dimensional superintegrable potential. These superintegrable potentials are the isotropic singular oscillator, the Holt potential, and the Coulomb potential. In all cases, a nontrivial space of nonconstant curvature is generated. We can study free motion and the motion with an additional superintegrable potential. For possible bound-state solutions, we find in all three cases an equation of the eighth order in the energy E. The special cases of the Darboux spaces are easily recovered by choosing the parameters accordingly. The text was submitted by the authors in English.     

On Quantum Phase Transition. I. Spinless Electrons Strongly Correlated with Ions

We study a large class F of models of the quantum statistical mechanics dealing with two types of particles. First the spinless electrons are quantum particles obeying to the Fermi statistics, they can hop. Secondly the ions which cannot move, are classical particles. The Falicov–Kimball (FK) model⁽¹⁾ is a well known model belonging to F, for which the existence of an antiferomagnetic phase transition was proven in the seminal paper of Kennedy and Lieb.⁽²⁾ This result was extended by Lebowitz and Macris.⁽³⁾ A new approach to this problem based on quantum selection of the ground states was proposed in ref. 4. In this paper we extend this approach to show that, under the strong insulating condition, any hamiltonian of the class F admits, at every temperature, an effective hamiltonian, which governs the behaviour of the ions interacting through forces mediated by the electrons. The effective hamiltonians are long range many body Ising hamiltonians, which can be computed by a cluster expansion expressed in term of the quantum fluctuations. Our main result is that we can apply the powerfull results of the classical statistical mechanics to our quantum models. In particular we can use the classical Pirogov–Sinai theory to establish a hierarchy of phase diagrams, we can also study of the behaviour of the quantum inter- faces,⁽²⁹⁾ and so on...     

Design and Analysis of InGaN-GaN Modulation Doped Field-Effect Transistors (MODFETs) for Over 60 GHz Operation

A Modulation-Doped Field-Effect Transistor (MODFET) structure realized in InGaN-GaN material system is presented for the first time. An analytical model predicting the transport characteristics of the proposed MODFET structure is given in detail. Electron energy levels inside and outside the quantum well channel of the MODFET are evaluated. The two-dimensional electron gas (2DEG) density in the channel is calculated by self-consistently solving Schrödinger and Poisson's equations simultaneously. Analytical results of the current-voltage and transconductance characteristics are presented. The unity-current gain cutoff frequency (f _T) of the proposed device is computed as a function of the gate voltage V _G . The results are compared well with experimental f _T value of a GaN/AlGaN HFET device. By scaling the gate length down to 0.25 m the proposed InGaN-GaN MODFET can be operated up to about 80GHz. It is shown in this paper that InGaN-GaN system has small degradation in f _T as the operating temperature is increased from 300°K to 400°K.     

Fractional Spin of System with Chern–Simons Term Coupled to Polaron

The fractional spin of a system with Chern–Simons (CS) term coupled to a polaron at the quantum level is studied. The Faddeev–Senjanovic (FS) scheme for path-integral quantization of constrained Hamiltonian systems is applied. The quantal conserved angular momentum and the fractional spin at the quantum level of this system are presented based on the quantal Noether theorem. The fractional spin is also presented for the system with Maxwell kinetic term.     

Pulse propagation of acoustic waves scattered in a three-dimensional channel

Abstract

In a previous paper (Whitman et al 1999 Waves Random Media 9 1–11) we discussed the scattering of acoustic waves by random sound-speed fluctuations in a two-dimensional channel and presented an asymptotic form for an acoustic pulse propagating in the channel. Here we include the three-dimensional effect of transverse scattering. We find an asymptotic solution in which initially the two-dimensional mode-transfer effect is more important than the transverse scattering effect. However, for large enough propagation distances the transverse scattering effect dominates the pulse spread. In this paper we shall show the form of the pulse shape in both propagation ranges as well as in the transition regime. We shall begin with a discussion of the physics of the problem and then present a mathematical discussion.     

Resummation of Mass Terms in Perturbative Massless Quantum Field Theory

The neutral massless scalar quantum field Φ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.