Generalized KdV equation for fluid dynamics and quantum algebras

We generalize the nonlinear one-dimensional equation of a fluid layer for any depth and length as an infinite-order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution written as a power series expansion with coefficients satisfying a nonlinear recurrence relation. In the limit of long and shallow water (shallow channels) we reobtain the well-known KdV equation together with its single-soliton solution.This article is dedicated to Max Jammer on the occasion of his 80th birthday. He is a clear friend, who was a visiting professor at the Johann Wolfgang Goethe-University in 1985. His brilliant lectures on Philosophische Probleme der modernen Physik, delivered in perfect German language, will long be remembered. Above all, Max Jammer's contributions to the philosophy of science have enriched our understanding forever.     

Quantum dynamics of cold trapped ions with application to quantum computation

Received: 10 March 1997/Revised version: 10 July 1997     

An electron fluid model for the lattice dynamics of metals

An electron fluid model is proposed for the lattice dynamics of metals which satisfies the requirement of translational invariance and the lattice is in equilibrium without recourse to external forces. The model is applied to calculate the phonon dispersion of sodium in the symmetry directions.     

Chaos,thermodynamics and quantum mechanics: an application to celestial dynamics

We address the issue of the quantum-classical correspondence in chaotic systems using, as recently done Zurek [Phys. Scr. T 76 (1998) 186], the solar system as a whole as a case study: this author shows that the classicality of the planetary motion is ensured by the environment-induced decoherence. We show that equivalent results are provided by the theories of spontaneous fluctuations and that these latter theories, in some cases, result in a still faster process of decoherence. We show that, as an additional benefit, the assumption of spontaneous fluctuation makes it possible to genuinely derive thermodynamics from mechanics, namely, without implicitly assuming thermodynamics.     

用精确的量子力学方法研究N + OD反应的动力学性质

采用close coupling (CC)方法,在3A’’势能面上[Guadagnini R, Schatz G C, Walch S P. Global potential energy surface for the lowest 1A’, 3A’’, and 1A’’ states of HNO [J]. J. Chem. Phys., 1995,10:774],我们利用量子含时波包方法对N + OH的同位素反应—N + OD进行了研究。在0.0-0.8 eV的平动能范围内,选态的反应几率受共振结构支配。利用 -shifting方法计算,我们得到了基态的速率常数,并对分子间的同位素效应进行了研究。     

Field-induced dynamics in the quantum Brownian oscillator: An exact treatment

We consider a quantum linear oscillator coupled to a bath in equilibrium at an arbitrary temperature and then exposed to an external field arbitrary in form and strength. We then derive the reduced density operator in closed form of the coupled oscillator in a non-equilibrium state at an arbitrary time.     

Assessing non-Markovian quantum dynamics

We investigate what a snapshot of a quantum evolution--a quantum channel reflecting open system dynamics--reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of "Markovianity" is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations.     

Far-from-equilibrium quantum many-body dynamics

A theory of real-time quantum many-body dynamics is evaluated in detail. It is based on a generating functional of correlation functions where the closed time contour extends only to a given time. Expanding the contour from this time to a later time leads to a dynamic flow of the generating functional. This flow describes the dynamics of the system and has an explicit causal structure. In the present work it is evaluated within a vertex expansion of the effective action leading to time-evolution equations for Green functions. These equations are applicable for strongly interacting systems as well as for studying the late-time behavior of non-equilibrium time evolution. For the specific case of a bosonic $\mathcal{N}$ -component φ ⁴-theory with contact interactions an s-channel truncation is identified to yield equations identical to those derived from the 2PI effective action in next-to-leading order of a $1/\mathcal{N}$ expansion. The presented approach allows to directly obtain non-perturbative dynamic equations beyond the widely used 2PI approximations.     

Cryogenic fluid dynamics

Ultrahigh Reynolds (Re) and Rayleigh (Ra) number flow can be produced and studied under controlled laboratory conditions using cryogenic liquid and gaseous He. Recent results on Rayleigh–Benard convection, pipe flow and towed grid turbulence are discussed together with some aspects of the future development.     

Nuclear fluid dynamics

For energies where the mean free nucleon path is comparable to the nuclear size, there is no fast local relaxation in nuclear collective motion. Therefore, in a fluid-dynamical approach, the intrinsic energy-density functional must take the distortion of the local Fermi surface into account. This can be achieved by a dynamical Thomas Fermi method which leads to additional restoring forces for the collective modes, except for the casesL=0 andL=1 where usual hydrodynamics is sufficient.     

Nuclear quantum many-body dynamics

A summary of recent researches on nuclear dynamics with realistic microscopic quantum approaches is presented. The Balian-Vénéroni variational principle is used to derive the time-dependent Hartree-Fock (TDHF) equation describing the dynamics at the mean-field level, as well as an extension including small-amplitude quantum fluctuations which is equivalent to the time-dependent random-phase approximation (TDRPA). Such formalisms as well as their practical implementation in the nuclear physics framework with modern three-dimensional codes are discussed. Recent applications to nuclear dynamics, from collective vibrations to heavy-ion collisions are presented. Particular attention is devoted to the interplay between collective motions and internal degrees of freedom. For instance, the harmonic nature of collective vibrations is questioned. Nuclei are also known to exhibit superfluidity due to pairing residual interaction. Extensions of the theoretical approach to study such pairing vibrations are now available. Large amplitude collective motions are investigated in the framework of heavy-ion collisions leading, for instance, to the formation of a compound system. How fusion is affected by the internal structure of the collision partners, such as their deformation, is discussed. Other mechanisms in competition with fusion, and responsible for the formation of fragments which differ from the entrance channel (transfer reactions, deep-inelastic collisions, and quasi-fission) are investigated. Finally, studies of actinide collisions forming, during very short times of few zeptoseconds, the heaviest nuclear systems available on Earth, are presented.     

Two-dimensional noncommutative quantum dynamics

This paper gives the two-dimensional extension for the noncommutative quantum dynamics of Rembielinski and Smolinski.     

Theory of quantum dynamics in fermionic environment: An influence functional approach

Quantum dynamics of a particle coupled to a fermionic environment is considered, with particular emphasis on the formulation of macroscopic quantum phenomena. The framework is based on a path integral formalism for the real-time density matrix. After integrating out of the fermion variables of the environment, we embed the whole environmental effects on the particle into the so-called influence functional in analogy to Feynman and Vernon's initial work. We then show that to the second order of the coupling constant, the exponent of the influence functional is in exact agreement with that due to a linear dissipative environment (boson bath). Having obtained this, we turn to a specific model in which the influence functional can be exactly evaluated in a long-time limit (long compared to the inverse of the cutoff frequency of the environmental spectrum). In this circumstance, we mainly address our attention to the quantum mechanical representation of the system-plus-environment from the known classical properties of the particle. It is shown that, in particular, the equivalence between the fermion bath and the boson bath is generally correct for a singlechannel coupling provided we make a simple mapping between the nonlinear interaction functions of the baths. Finally, generalizations of the model to more complicated situations are discussed and significant applications and connections to certain practically interesting problems are mentioned.     

An application of ideal experiments to quantum mechanical measurement theory

It is shown that the rule for obtaining probabilities by squaring amplitudes is deducible from ideal experiments in a mechanics of unitary motion in a complex-linear space, with tensor product for making compound systems. Difficulty with tensor product in undoctored quaternionic quantum mechanics makes the argument inapplicable there. Except for the replacement by ideal experiments of a more formal unitary equivalence, the discussion is similar to that of Everett (1957). Diagonal expression of a general vector in the tensor product of two spaces is related to polar form of a matrix, in the Appendix.     

Direct characterization of quantum dynamics

The characterization of quantum dynamics is a fundamental and central task in quantum mechanics. This task is typically addressed by quantum process tomography (QPT). Here we present an alternative "direct characterization of quantum dynamics" (DCQD) algorithm. In contrast to all known QPT methods, this algorithm relies on error-detection techniques and does not require any quantum state tomography. We illustrate that, by construction, the DCQD algorithm can be applied to the task of obtaining partial information about quantum dynamics. Furthermore, we argue that the DCQD algorithm is experimentally implementable in a variety of prominent quantum-information processing systems, and show how it can be realized in photonic systems with present day technology.     

Properties of modified quantum dynamics

The general nature of the dynamics that can be described by an equation for the density matrix of nonrelativistic quantum systems previously proposed by us [1] is studied. It is shown that it leads to an experimentally observed constraint on the states of the microscopic and quasi-macroscopic systems by states that can be described by more or less localized wave packets in phase space and replaces the ordinary spreading of these packets by statistically deterministic transitions between corresponding states. This makes possible a purely dynamic solution of the problem of the classical object and of the problem of measurement in quantum mechanics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 63–67, May, 1976.I wish to express my deep appreciation to Prof. V. G. Bagrov for his interest in the study and for criticism.     

Lattice dynamics of quantum crystals

A theory of lattice dynamics for quantum crystals is developed. This is done by summing an infinite class of diagrams of the usual anharmonic expansion and by avoiding the harmonic approximation as starting point. The zero order of the expansion given in this paper corresponds to the harmonic approximation with an effective potential. Higher orders correspond to higher anharmonic corrections with the same potential. Since the new potential varies more slowly the expansion seems to converge more rapidly than the usual anharmonic expansion. Numerical calculations on bcc He³ show that the ground state energy is lowered by about 3–4 cal/mol by taking into account long range correlations due to phonons. The elastic constants and the Debye temperature are calculated in zero and second order. The lowering of the bulk modulus due to the second order is about 10%. Experiments agree quite well with the second order results.     

An application of Bell's inequalities to a quantum state extension problem

Using techniques from the study of quantum violations of Bell's inequalities, we give examples of three C ^*-algebras A, B, C, and states ₁₂ on A B, and ₂₃ on B C, which agree on B, but do not have a common extension to A B C. This situation cannot occur in classical probability, i.e. for commutative algebras.