Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions
International Nuclear Information System (INIS)
Hu, B.L.; Matacz, A.
1994-01-01
The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes such as decoherence, dissipation, particle creation, noise, and fluctuation. The present paper continues the investigation begun in earlier papers on the quantum Brownian motion in a general environment via the influence functional formalism. Here, the Brownian particle is coupled linearly to a bath of the most general time-dependent quadratic oscillators. This bath of parametric oscillators minics a scalar field, while the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode, or the scale factor of the Universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients, thus setting the stage for the influence functional formalism treatment of problems in quantum field theory in curved spacetime. This method enables one to trace the source of statistical processes such as decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh, and Gibbons and Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and back reaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics
Presentation of quantum Brownian movement in the collective coordinate method
International Nuclear Information System (INIS)
Oksak, A.I.; Sukhanov, A.D.
2003-01-01
Two explicitly solved models of quantum randomized processes described by the Langevin equation, i. e. a free quantum Brownian particle and a quantum Brownian harmonic oscillator, are considered. The Hamiltonian (string) realization of the models reveals soliton-like structure of classical solutions. Accordingly, the method of zero mode collective coordinate is an adequate means for describing the models quantum dynamics [ru
Brownian parametric oscillators
Zerbe, Christine; Jung, Peter; Hänggi, Peter
1994-05-01
We discuss the stochastic dynamics of dissipative, white-noise-driven Floquet oscillators, characterized by a time-periodic stiffness. Thus far, little attention has been paid to these exactly solvable nonstationary systems, although they carry a rich potential for several experimental applications. Here, we calculate and discuss the mean values and variances, as well as the correlation functions and the Floquet spectrum. As one main result, we find for certain parameter values that the fluctuations of the position coordinate are suppressed as compared to the equilibrium value of a harmonic oscillator (parametric squeezing).
Decay ratio for third order Brownian oscillators
International Nuclear Information System (INIS)
Konno, H.; Kanemoto, S.
1998-01-01
We have obtained the analytical expressions of the decay ratios for two types of third order Brownian oscillators which are generalizations of the second order Brownian oscillator driven by the Gaussian-white noise. The resulting expressions will provide us useful baseline information for more complicated practical problems and their applications
Quantum equations from Brownian motions
International Nuclear Information System (INIS)
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Quantum description of the Brownian movement in an external field
International Nuclear Information System (INIS)
Svin'in, I.R.
1976-01-01
The Schroedinger equation for brownian motion in an external field is obtained on the basis of the classical Langevin equation. The specific features of the approach proposed are illustrated by the example of the brownian motion of the quantum oscillator. The influence of the fluctuations on the various physical quantities is considered
The open quantum Brownian motions
International Nuclear Information System (INIS)
Bauer, Michel; Bernard, Denis; Tilloy, Antoine
2014-01-01
Using quantum parallelism on random walks as the original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers—with internal degrees of freedom which serve as random gyroscopes—interacting with a series of probes which serve as quantum coins. These processes may also be viewed as the scaling limit of open quantum random walks and we develop this approach along three different lines: the quantum trajectory, the quantum dynamical map and the quantum stochastic differential equation. We also present a study of the simplest case, with a two level system as an internal gyroscope, illustrating the interplay between the ballistic and diffusive behaviors at work in these processes. Notation H z : orbital (walker) Hilbert space, C Z in the discrete, L 2 (R) in the continuum H c : internal spin (or gyroscope) Hilbert space H sys =H z ⊗H c : system Hilbert space H p : probe (or quantum coin) Hilbert space, H p =C 2 ρ t tot : density matrix for the total system (walker + internal spin + quantum coins) ρ-bar t : reduced density matrix on H sys : ρ-bar t =∫dxdy ρ-bar t (x,y)⊗|x〉 z 〈y| ρ-hat t : system density matrix in a quantum trajectory: ρ-hat t =∫dxdy ρ-hat t (x,y)⊗|x〉 z 〈y|. If diagonal and localized in position: ρ-hat t =ρ t ⊗|X t 〉 z 〈X t | ρ t : internal density matrix in a simple quantum trajectory X t : walker position in a simple quantum trajectory B t : normalized Brownian motion ξ t , ξ t † : quantum noises (paper)
Quantum Brownian motion model for the stock market
Meng, Xiangyi; Zhang, Jian-Wei; Guo, Hong
2016-06-01
It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysical framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system-a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics.
Quantum Darwinism in Quantum Brownian Motion
Blume-Kohout, Robin; Zurek, Wojciech H.
2008-12-01
Quantum Darwinism—the redundant encoding of information about a decohering system in its environment—was proposed to reconcile the quantum nature of our Universe with apparent classicality. We report the first study of the dynamics of quantum Darwinism in a realistic model of decoherence, quantum Brownian motion. Prepared in a highly squeezed state—a macroscopic superposition—the system leaves records whose redundancy increases rapidly with initial delocalization. Redundancy appears rapidly (on the decoherence time scale) and persists for a long time.
Quantum dynamical framework for Brownian heat engines
Agarwal, G. S.; Chaturvedi, S.
2013-07-01
We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.
Thermodynamic and Quantum Thermodynamic Analyses of Brownian Movement
Gyftopoulos, Elias P.
2006-01-01
Thermodynamic and quantum thermodynamic analyses of Brownian movement of a solvent and a colloid passing through neutral thermodynamic equilibrium states only. It is shown that Brownian motors and E. coli do not represent Brownian movement.
International Nuclear Information System (INIS)
Svin'in, I.R.
1982-01-01
The Brownian motion of a quadrupole quantum oscillator is considered as a model of surface quadrupole oscillations of heated spherical nuclei. The integrals of the motion related to energy and angular momentum conservation are constructed and the wave functions are obtained for states with definite values of these integrals of the motion in the phonon representation
The quantum brownian particle and memory effects
International Nuclear Information System (INIS)
Britani, J.R.; Mizrahi, S.S.; Pimentel, B.M.
1991-01-01
The Quantum Brownian particle, immersed in a heat bath, is described by a statistical operator whose evolution is ruled by a Generalized Master Equation (GME). The heat bath degrees of freedom are considered to be either white noise or coloured noise correlated,while the GME is considered under either the Markov or Non-Markov approaches. The comparison between these considerations are fully developed and their physical meaning is discussed. (author)
QUANTUM STOCHASTIC PROCESSES: BOSON AND FERMION BROWNIAN MOTION
Directory of Open Access Journals (Sweden)
A.E.Kobryn
2003-01-01
Full Text Available Dynamics of quantum systems which are stochastically perturbed by linear coupling to the reservoir can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation. In order to work it out one needs to define the quantum Brownian motion. As far as only its boson version has been known until recently, in the present paper we present the definition which makes it possible to consider the fermion Brownian motion as well.
Microscopic derivation of open quantum Brownian motion: a particular example
International Nuclear Information System (INIS)
Sinayskiy, Ilya; Petruccione, Francesco
2015-01-01
The microscopic derivation of a new type of Brownian motion, namely open quantum Brownian motion (OQBM) is presented. The quantum master equation for OQBM is derived for a weakly driven system interacting with a decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. Both examples demonstrate convergence of the OQBM dynamics to Gaussian distributions. (topical article)
Quantum work fluctuation theorem: Nonergodic Brownian motion case
International Nuclear Information System (INIS)
Bai, Zhan-Wu
2014-01-01
The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
International Nuclear Information System (INIS)
Yeh, L.
1993-01-01
After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented
Under which conditions is quantum Brownian motion observable in a microscope?
International Nuclear Information System (INIS)
Helseth, L.E.
2010-01-01
We investigate under which conditions we can expect to observe quantum Brownian motion in a microscope. Using the fluctuation-dissipation theorem, we investigate quantum Brownian motion in an ohmic bath, and estimate temporal and spatial accuracy required to observe a crossover from classical to quantum behavior.
Bose polaron as an instance of quantum Brownian motion
Directory of Open Access Journals (Sweden)
Aniello Lampo
2017-09-01
Full Text Available We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.
International Nuclear Information System (INIS)
Svin'in, I.R.
1982-01-01
Description of collective phenomena in heated nuclei within the framework of the Brownian approximation may be conditionally divided into two parts: 1) solution of the problem for some realization of a random force, 2) averaging in a set of all the possible realizations. Results of the present work are setted the first part of the problem in the case of surface quadrupole oscillations of spherical heated nuclei. Quadrupole surface oscillations of heated spherical nuclei are considered in the Brownian motion approximation. The integrals of motion are constructed taking into account the energy and angular momentum conservations for the nucleus in the process of relaxation of the collective excitations. Wave functions are obtained for states having definite values of the integrals of motion in the phonon representation. It is noted that the description scheme developed is easily used with respect to other multipolarity oscillations
International Nuclear Information System (INIS)
Shit, Anindita; Chattopadhyay, Sudip; Chaudhuri, Jyotipratim Ray
2012-01-01
Graphical abstract: By invoking physically motivated coordinate transformation into quantum Smoluchowski equation, we have presented a transparent treatment for the determination of the effective diffusion coefficient and current of a quantum Brownian particle. Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects. Highlights:: ► Transport of a quantum Brownian particle in a periodic potential has been addressed. ► Governing quantum Smoluchowski equation (QSE) includes state dependent diffusion. ► A coordinate transformation is used to recast QSE with constant diffusion. ► Transport properties increases in comparison to the corresponding classical result. ► This enhancement is purely a quantum effect. - Abstract: The transport property of a quantum Brownian particle that interacts strongly with a bath (in which a typical damping constant by far exceeds a characteristic frequency of the isolated system) under the influence of a tilted periodic potential has been studied by solving quantum Smoluchowski equation (QSE). By invoking physically motivated coordinate transformation into QSE, we have presented a transparent treatment for the determination of the effective diffusion coefficient of a quantum Brownian particle and the current (the average stationary velocity). Substantial enhancement in the efficiency of the diffusive transport is envisaged due to the quantum correction effects only if the bath temperature hovers around an appropriate range of intermediate values. Our findings also confirm the results obtained in the classical cases.
Large quantum dots with small oscillator strength
DEFF Research Database (Denmark)
Stobbe, Søren; Schlereth, T.W.; Höfling, S.
2010-01-01
We have measured the oscillator strength and quantum efficiency of excitons confined in large InGaAs quantum dots by recording the spontaneous emission decay rate while systematically varying the distance between the quantum dots and a semiconductor-air interface. The size of the quantum dots...... is measured by in-plane transmission electron microscopy and we find average in-plane diameters of 40 nm. We have calculated the oscillator strength of excitons of that size assuming a quantum-dot confinement given by a parabolic in-plane potential and a hard-wall vertical potential and predict a very large...... intermixing inside the quantum dots....
Quantum electronics maser amplifiers and oscillators
Fain, V M; Sanders, J H
2013-01-01
Quantum Electronics, Volume 2: Maser Amplifiers and Oscillators deals with the experimental and theoretical aspects of maser amplifiers and oscillators which are based on the principles of quantum electronics. It shows how the concepts and equations used in quantum electronics follow from the basic principles of theoretical physics.Comprised of three chapters, this volume begins with a discussion on the elements of the theory of quantum oscillators and amplifiers working in the microwave region, along with the practical achievements in this field. Attention is paid to two-level paramagnetic ma
Non-Markovian quantum Brownian motion in one dimension in electric fields
Shen, H. Z.; Su, S. L.; Zhou, Y. H.; Yi, X. X.
2018-04-01
Quantum Brownian motion is the random motion of quantum particles suspended in a field (or an effective field) resulting from their collision with fast-moving modes in the field. It provides us with a fundamental model to understand various physical features concerning open systems in chemistry, condensed-matter physics, biophysics, and optomechanics. In this paper, without either the Born-Markovian or rotating-wave approximation, we derive a master equation for a charged-Brownian particle in one dimension coupled with a thermal reservoir in electric fields. The effect of the reservoir and the electric fields is manifested as time-dependent coefficients and coherent terms, respectively, in the master equation. The two-photon correlation between the Brownian particle and the reservoir can induce nontrivial squeezing dynamics to the particle. We derive a current equation including the source from the driving fields, transient current from the system flowing into the environment, and the two-photon current caused by the non-rotating-wave term. The presented results then are compared with that given by the rotating-wave approximation in the weak-coupling limit, and these results are extended to a more general quantum network involving an arbitrary number of coupled-Brownian particles. The presented formalism might open a way to better understand exactly the non-Markovian quantum network.
Quantum oscillations of conductivity in bismuth wires
International Nuclear Information System (INIS)
Condrea, Elena
2011-01-01
Measurements of the resistance of bismuth nanowires with several diameters and different quality reveal oscillations on the dependence of resistance under uniaxial strain at T = 4.2 K. Amplitude of oscillations is significant (38 %) at helium temperature and becomes smearing at T = 77 K. Observed oscillations originate from quantum size effect. A simple evaluation of period of oscillations allows us to identify the groups of carriers involved in transport. Calculated periods of 42.2 and 25.9 nm satisfy approximately the ratio 2:1 for two experimentally observed sets of oscillations from light and heavy electrons.
Modeling stock return distributions with a quantum harmonic oscillator
Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.
2017-11-01
We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.
Relativistic Brownian motion and the foundations of quantum mechanics
International Nuclear Information System (INIS)
Roy, S.
1979-01-01
Within the context of the generalized stochastic interpretation of quantum mechanics it is possible to deduce the quantum principles as well as to resolve the EPR paradox. Moreover, the postulates of the stochastic space-time as proposed by Frederick et al. can be deduced in a consistent way. A new possibility arises of rethinking of the existence of hidden variables in quantum mechanics
Stripes instability of an oscillating non-Brownian iso-dense suspension of spheres
Roht, Y. L.; Ippolito, I.; Hulin, J. P.; Salin, D.; Gauthier, G.
2018-03-01
We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap H. We do observe an instability of the initially homogeneous concentration in the form of concentration variation stripes transverse to the flow. The wavelength of these regular spatial structures scales roughly as the gap of the cell and is independent of the particle concentration and of the period of oscillation. This instability requires large enough particle volume fractions φ≥ 0.25 and a gap large enough compared to the sphere diameter (H/d ≥ 8) . Mapping the domain of the existence of this instability in the space of the control parameters shows that it occurs only in a limited range of amplitudes of the fluid displacement. The analysis of the concentration distribution across the gap supports a scenario of particle migration towards the wall followed by an instability due to a particle concentration gradient with a larger concentration at the walls. In order to account for the main features of this stripes instability, we use the theory of longitudinal instability due to normal stresses difference and recent observations of a dependence of the first normal stresses difference on the particle concentration.
'quantumness' measures in the decohering harmonic oscillator
Indian Academy of Sciences (India)
We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of ...
QUANTUM THEORY OF DAMPED HARMONIC OSCILLATOR
African Journals Online (AJOL)
DJFLEX
However, the problem of quantum oscillator with time-varying frequency had been solved (Um et al,. 1987). The Hamiltonian of this model is usually quadratic in co-ordinates and momentum operators (Ikot et al, 2008). The quantum calculation is applied because it will give the information about the particle at intermediate ...
Relativistic Brownian motion and the foundations of quantum mechanics
International Nuclear Information System (INIS)
Roy, S.
1979-01-01
Within the context of the generalized stochastic interpretation of quantum mechanics it is possible to deduce the quantum principles as well as to resolve the EPR paradox. Moreover, the postulates of the stochastic space-time as proposed by Frederick et al. can be deduced in a consistent way. A new possibility arises of rethinking of the existence of hidden variables in quantum mechanics. (author)
The macroscopic harmonic oscillator and quantum measurements
International Nuclear Information System (INIS)
Hayward, R.W.
1982-01-01
A quantum mechanical description of a one-dimensional macroscopic harmonic oscillator interacting with its environment is given. Quasi-coherent states are introduced to serve as convenient basis states for application of a density matrix formalism to characterize the system. Attention is given to the pertinent quantum limits to the precision of measurement of physical observables that may provide some information on the nature of a weak classical force interacting with the oscillator. A number of ''quantum nondemolition'' schemes proposed by various authors are discussed. (Auth.)
Theory of a quantum anharmonic oscillator
International Nuclear Information System (INIS)
Carusotto, S.
1988-01-01
The time evolution of a quantum single-quartic anharmonic oscillator is considered. The study is carried on in operational form by use of the raising and lowering operators of the oscillator. The equation of motion is solved by application of a new integration method based on iteration techniques, and the rigorous solutions that describe the time development of the displacement and momentum operators of the oscillator are obtained. These operators are presented as a Laplace transform and a subsequent inverse Laplace transform of suitable functionals. Finally, the results are employed to describe the time evolution of a quasiclassical anharmonic oscillator
Introduction to Classical and Quantum Harmonic Oscillators
International Nuclear Information System (INIS)
Latal, H
1997-01-01
As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)
Voltage-driven quantum oscillations in graphene
International Nuclear Information System (INIS)
Yampol'skii, V A; Savel'ev, S; Nori, Franco
2008-01-01
We predict unusual (for non-relativistic quantum mechanics) electron states in graphene, which are localized within a finite-width potential barrier. The density of localized states in the sufficiently high and/or wide graphene barrier exhibits a number of singularities at certain values of the energy. Such singularities provide quantum oscillations of both the transport (e.g. conductivity) and thermodynamic properties of graphene-when increasing the barrier height and/or width, similarly to the well-known Shubnikov-de-Haas (SdH) oscillations of conductivity in pure metals. However, here the SdH-like oscillations are driven by an electric field instead of the usual magnetically driven SdH-oscillations
Quantum damped oscillator I: Dissipation and resonances
International Nuclear Information System (INIS)
Chruscinski, Dariusz; Jurkowski, Jacek
2006-01-01
Quantization of a damped harmonic oscillator leads to so called Bateman's dual system. The corresponding Bateman's Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states which are responsible for the irreversible quantum dynamics of a damped harmonic oscillator
Quantum electrodynamical torques in the presence of Brownian motion
Munday, J. N.; Iannuzzi, D.; Capasso, F.
2006-01-01
Quantum fluctuations of the electromagnetic field give rise to a zero-point energy that persists even in the absence of electromagnetic sources. One striking consequence of the zero-point energy is manifested in the Casimir force, which causes two electrically neutral metallic plates to attract in
Brownian quasi-particles and quantum quasi-particles
International Nuclear Information System (INIS)
Fronteau, J.
1987-01-01
The concept of quasi-particles is used in Statistical Mechanics as well as in Quantum Mechanics, to associate differentiable trajectories to the equations of evolution, trajectories on which a maximum of informations is concentrated concerning the phenomena studied. Two cases are treated numerically, that of the Fokker-Planck equation with an x - x 3 field, and that of the Schroedinger equation with null potential, in a situation of interference [fr
Computing With Quantum Mechanical Oscillators
National Research Council Canada - National Science Library
Parks, A
1991-01-01
Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations...
A quantum harmonic oscillator and strong chaos
International Nuclear Information System (INIS)
Oprocha, Piotr
2006-01-01
It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models
International Nuclear Information System (INIS)
Allahverdyan, A.E.; Khrennikov, A.; Nieuwenhuizen, Th.M.
2005-01-01
For two classical Brownian particles an analog of continuous-variable quantum entanglement is presented: The common probability distribution of the two coordinates and the corresponding coarse-grained velocities cannot always be prepared via mixing of any factorized distributions referring to the two particles separately. This is possible for particles which have interacted in the past, but do not interact at present. Three factors are crucial for the effect: (1) separation of time scales of coordinate and momentum which motivates the definition of coarse-grained velocities; (2) the resulting uncertainty relations between the coordinate of the Brownian particle and the change of its coarse-grained velocity; (3) the fact that the coarse-grained velocity, though pertaining to a single Brownian particle, is defined on a common context of two particles. The Brownian entanglement is a consequence of a coarse-grained description and disappears for a finer resolution of the Brownian motion. Analogies with the quantum situation are discussed, as well as possibilities of experimental realization of the effect in examples of macroscopic Brownian motion
Boltzmann map for quantum oscillators
International Nuclear Information System (INIS)
Streater, R.F.
1987-01-01
The authors define a map tau on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points of tau. The map tau is the composition of a double stochastic map T*, and the quasifree reduction Q. Under mixing conditions on T, iterates of tau take any initial state to the Gibbs states, provided that the oscillator frequencies are mutually rational. They give an example of a system with three degrees of freedom with energies omega 1 , omega 2 , and omega 3 mutually irrational, but obeying a relation n 1 omega 1 + n 2 omega 2 = n 3 omega 3 , n/sub i/epsilon Z. The iterated Boltzmann map converges from an initial state rho to independent Gibbs states of the three oscillators at betas (inverse temperatures) β 1 , β 2 , β 3 obeying the equation n 1 omega 1 β 1 + n 2 omega 3 β 1 number. The equilibrium state can be rewritten as a grand canonical state. They show that for two, three, or four fermions we can get the usual rate equations as a special case
Revealing virtual processes of a quantum Brownian particle in phase space
International Nuclear Information System (INIS)
Maniscalco, S
2005-01-01
The short-time dynamics of a quantum Brownian particle in a harmonic potential is studied in phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the Wigner function of an initially squeezed state is analysed. It is shown that virtual exchanges of energy between the particle and the reservoir, characterizing the non-Lindblad short-time dynamics where system-reservoir correlations are not negligible, show up in phase space
Quantum oscillators in the canonical coherent states
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Lima, A.F. de; Ferreira, K. de Araujo [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Fisica; Vaidya, A.N. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
2001-11-01
The main characteristics of the quantum oscillator coherent states including the two-particle Calogero interaction are investigated. We show that these Calogero coherent states are the eigenstates of the second-order differential annihilation operator which is deduced via Wigner-Heisenberg algebraic technique and correspond exactly to the pure uncharged-bosonic states. They posses the important properties of non-orthogonality and completeness. The minimum uncertainty relation for the Wigner oscillator coherent states are investigated. New sets of even and odd coherent states are point out. (author)
Quantum information, oscillations and the psyche
Martin, F.; Carminati, F.; Galli Carminati, G.
2010-05-01
In this paper, taking the theory of quantum information as a model, we consider the human unconscious, pre-consciousness and consciousness as sets of quantum bits (qubits). We view how there can be communication between these various qubit sets. In doing this we are inspired by the theory of nuclear magnetic resonance. In this way we build a model of handling a mental qubit with the help of pulses of a mental field. Starting with an elementary interaction between two qubits we build two-qubit quantum logic gates that allow information to be transferred from one qubit to the other. In this manner we build a quantum process that permits consciousness to "read" the unconscious and vice versa. The elementary interaction, e.g. between a pre-consciousness qubit and a consciousness one, allows us to predict the time evolution of the pre-consciousness + consciousness system in which pre-consciousness and consciousness are quantum entangled. This time evolution exhibits Rabi oscillations that we name mental Rabi oscillations. This time evolution shows how for example the unconscious can influence consciousness. In a process like mourning the influence of the unconscious on consciousness, as the influence of consciousness on the unconscious, are in agreement with what is observed in psychiatry.
Quantum oscillations in nodal line systems
Yang, Hui; Moessner, Roderich; Lim, Lih-King
2018-04-01
We study signatures of magnetic quantum oscillations in three-dimensional nodal line semimetals at zero temperature. The extended nature of the degenerate bands can result in a Fermi surface geometry with topological genus one, as well as a Fermi surface of electron and hole pockets encapsulating the nodal line. Moreover, the underlying two-band model to describe a nodal line is not unique, in that there are two classes of Hamiltonian with distinct band topology giving rise to the same Fermi-surface geometry. After identifying the extremal cyclotron orbits in various magnetic field directions, we study their concomitant Landau levels and resulting quantum oscillation signatures. By Landau-fan-diagram analyses, we extract the nontrivial π Berry phase signature for extremal orbits linking the nodal line.
Remote quantum entanglement between two micromechanical oscillators.
Riedinger, Ralf; Wallucks, Andreas; Marinković, Igor; Löschnauer, Clemens; Aspelmeyer, Markus; Hong, Sungkun; Gröblacher, Simon
2018-04-01
Entanglement, an essential feature of quantum theory that allows for inseparable quantum correlations to be shared between distant parties, is a crucial resource for quantum networks 1 . Of particular importance is the ability to distribute entanglement between remote objects that can also serve as quantum memories. This has been previously realized using systems such as warm 2,3 and cold atomic vapours 4,5 , individual atoms 6 and ions 7,8 , and defects in solid-state systems 9-11 . Practical communication applications require a combination of several advantageous features, such as a particular operating wavelength, high bandwidth and long memory lifetimes. Here we introduce a purely micromachined solid-state platform in the form of chip-based optomechanical resonators made of nanostructured silicon beams. We create and demonstrate entanglement between two micromechanical oscillators across two chips that are separated by 20 centimetres . The entangled quantum state is distributed by an optical field at a designed wavelength near 1,550 nanometres. Therefore, our system can be directly incorporated in a realistic fibre-optic quantum network operating in the conventional optical telecommunication band. Our results are an important step towards the development of large-area quantum networks based on silicon photonics.
Quantum gravity signals in neutrino oscillations
International Nuclear Information System (INIS)
Sprenger, M.; Nicolini, P.; Bleicher, M.
2011-01-01
We investigate the effect of a Quantum Gravity-induced minimal length on neutrino oscillations. The minimal length is implemented in a phenomenological framework, allowing us to make predictions independently of any fundamental approach. We obtain clear minimal length signatures and discuss their observability in current and future experiments. We present an overview over other scenarios in which the minimal length leaves its signature and show new results concerning minimal length thermodynamics. (author)
International Nuclear Information System (INIS)
Sukhanov, A.D.
2004-01-01
Generalized correlations of the Schroedinger indefinitenesses are shown to have the meaning of the fundamental restrictions as to characteristics of space of states in any probability-like theory. Quantum mechanics, as well as, theory of the brownian movement at arbitrary space of time fall in the category of the mentioned theories. One compared correlations of coordinates-pulse indefinitenesses within the mentioned theory with the similar correlation of indefinitenesses for microparticle under the Gaussian wave packet state. One determined that in case of profound distinction in mathematical tools of two theories one observes their conceptual resemblance. It manifests itself under the alternative conditions - short times in one theory correspond to long ones in another theory and vice versa, while in any of the mentioned theories uncontrollable effect of either quantum or thermal type is of crucial importance [ru
Quantum theory of anharmonic oscillators
International Nuclear Information System (INIS)
Yamazaki, K.; Kyoto Univ.
1983-01-01
This in investigation of an anharmonic oscillator characterized by the potential ωsub(o) 2 /2 g 2 + lambda'q 4 . By using the equations of motion and the relations obtained by evaluating where O is an arbitrary operator, H is our total Hamiltonian and |i> and |j> are exact eigenstates of H, we derive an exact recurrence formula. This formula allows us to express tau-functions with a higher power of the variables through tau-functions with a lower power of the variables and energy eigenvalues. In this way we derive several exact relations, which are, in a sense, generalizations of the virial theorem and sum rules. These exact relations are the central equations of this paper. On the basis of these exact relations we propose our 'nearest neighbour level' (N.N.L.) approximation, which seems to provide a good approximation scheme. We can also use our exact relations to test the validity of various approximation methods, and as an example, we discuss the 'New-Tamm-Dancoff' (N.T.D)-type of approximation in detail. (Author)
Rabi oscillations a quantum dot exposed to quantum light
International Nuclear Information System (INIS)
Magyarov, A.; Slepyan, G.Ya.; Maksimenko, S.A.; Hoffmann, A.
2007-01-01
The influence of the local field on the excitonic Rabi oscillations in an isolated quantum dot driven by the coherent state of light has been theoretically investigated. Local field is predicted to entail the appearance of two oscillatory regimes in the Rabi effect separated by the bifurcation. In the first regime Rabi oscillations are periodic and do not reveal collapse-revivals phenomenon, while in the second one collapse and revivals appear, showing significant difference as compared to those predicted by the standard Jaynes-Cummings model
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.
Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-22
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Quasi quantum group covariant q-oscillators
International Nuclear Information System (INIS)
Schomerus, V.
1992-05-01
If q is a p-th root of unity there exists a quasi-co-associative truncated quantum group algebra U T q (sl 2 ) whose indecomposable representations are the physical representations of U q (sl 2 ), whose co-product yields the truneated tensor product of physical representations of U q (sl 2 ), and whose R-matrix satisfies quasi Yang Baxter equations. For primitive p-th roots q, we consider a 2-dimensional q-oscillator which admits U T q (sl 2 ) as a symmetry algebra. Its wave functions lie in a space F T q of 'functions on the truncated quantum plane', i.e. of polynomials in noncommuting complex coordinate functions z a , on which multiplication operators Z a and the elements of U T q (sl 2 ) can act. This illustrates the concept of quasi quantum planes. Due to the truncation, the Hilbert space of states is finite dimensional. The subspaces F T(n) of monomials in x a of n-th degree vanish for n ≥ p-1, and F T(n) carries the 2J+1 dimensional irreducible representation of U T q (sl 2 ) if n=2J, J=0, 1/2, ... 1/2(p-2). Partial derivatives δ a are introduced. We find a *-operation on the algebra of multiplication operators Z i and derivatives δ b such that the adjoints Z * a act as differentiation on the truncated quantum plane. Multiplication operators Z a ('creation operators') and their adjoints ('annihilation operators') obey q -1/2 -commutation relations. The *-operation is used to determine a positive definite scalar product on the truncated quantum plane F T q . Some natural candidates of Hamiltonians for the q-oscillators are determined. (orig./HSI)
Coupled harmonic oscillators and their quantum entanglement
Makarov, Dmitry N.
2018-04-01
A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.
Quantum information, oscillations and the psyche
Martin, F; Carminati, G Galli
2010-01-01
In this paper, taking the theory of quantum information as a model, we consider the human unconscious, pre-consciousness and consciousness as sets of quantum bits (qubits). We view how there can be communication between these various qubit sets. In doing this we are inspired by the theory of nuclear magnetic resonance. In this way we build a model of handling a mental qubit with the help of pulses of a mental field. Starting with an elementary interaction between two qubits we build two-qubit quantum logic gates that allow information to be transferred from one qubit to the other. In this manner we build a quantum process that permits consciousness to ``read{''} the unconscious and vice versa. The elementary interaction, e.g. between a pre-consciousness qubit and a consciousness one, allows us to predict the time evolution of the pre-consciousness + consciousness system in which pre-consciousness and consciousness are quantum entangled. This time evolution exhibits Rabi oscillations that we name mental Rabi o...
Quantum oscillations in vortex-liquids
Banerjee, Sumilan; Zhang, Shizhong; Randeria, Mohit
2012-02-01
Motivated by observations of quantum oscillations in underdoped cuprates [1], we examine the electronic density of states (DOS) in a vortex-liquid state, where long-range phase coherence is destroyed by an external magnetic field H but the local pairing amplitude survives. We note that this regime is distinct from that studied in most of the recent theories, which have focused on either a Fermi liquid with a competing order parameter or on a d-wave vortex lattice. The cuprate experiments are very likely in a resistive vortex-liquid state. We generalize the s-wave analysis of Maki and Stephen [2] to d-wave pairing and examine various regimes of the chemical potential, gap and field. We find that the (1/H) oscillations of the DOS at the chemical potential in a d-wave vortex-liquid are much more robust, i.e., have a reduced damping, compared to the s-wave case. We critically investigate the conventional wisdom relating the observed frequency to the area of an underlying Fermi surface. We also show that the oscillations in the DOS cross over to a √H behavior in the low field limit, in agreement with the recent specific heat measurements. [1] L. Taillefer, J. Phys. Cond. Mat. 21, 164212 (2009). [2] M. J. Stephen, Phys. Rev. B 45, 5481 (1992).
International Nuclear Information System (INIS)
Chen Aimin; Cho Samyoung
2011-01-01
Conditional quantum oscillations are investigated for quantum gate operations in superconducting flux qubits. We present an effective Hamiltonian which describes a conditional quantum oscillation in two-qubit systems. Rabi-type quantum oscillations are discussed in implementing conditional quantum oscillations to quantum gate operations. Two conditional quantum oscillations depending on the states of control qubit can be synchronized to perform controlled-gate operations by varying system parameters. It is shown that the conditional quantum oscillations with their frequency synchronization make it possible to operate the controlled-NOT and -U gates with a very accurate gate performance rate in interacting qubit systems. Further, this scheme can be applicable to realize a controlled multi-qubit operation in various solid-state qubit systems. (author)
Neutrino oscillations in discrete-time quantum walk framework
Energy Technology Data Exchange (ETDEWEB)
Mallick, Arindam; Mandal, Sanjoy; Chandrashekar, C.M. [C. I. T. Campus, The Institute of Mathematical Sciences, Chennai (India); Homi Bhabha National Institute, Training School Complex, Mumbai (India)
2017-02-15
Here we present neutrino oscillation in the framework of quantum walks. Starting from a one spatial dimensional discrete-time quantum walk we present a scheme of evolutions that will simulate neutrino oscillation. The set of quantum walk parameters which is required to reproduce the oscillation probability profile obtained in both, long range and short range neutrino experiment is explicitly presented. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental set-up with access to control a single six-level system, a multiparticle three-qubit or a qubit-qutrit system. We also present the entanglement between spins and position space, during neutrino propagation that will quantify the wave function delocalization around instantaneous average position of the neutrino. This work will contribute towards understanding neutrino oscillation in the framework of the quantum information perspective. (orig.)
International Nuclear Information System (INIS)
Zhu, Ka-Di; Li, Wai-Sang
2003-01-01
The quantum coherent oscillations in a coherently driven quantum dot-cavity system with the presence of strong exciton-phonon interactions are investigated theoretically in a fully quantum treatment. It is shown that even at zero temperature, the strong exciton-phonon interactions still affect the quantum coherent oscillations significantly
Quantum correlations in terms of neutrino oscillation probabilities
Energy Technology Data Exchange (ETDEWEB)
Alok, Ashutosh Kumar, E-mail: akalok@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Banerjee, Subhashish, E-mail: subhashish@iitj.ac.in [Indian Institute of Technology Jodhpur, Jodhpur 342011 (India); Uma Sankar, S., E-mail: uma@phy.iitb.ac.in [Indian Institute of Technology Bombay, Mumbai 400076 (India)
2016-08-15
Neutrino oscillations provide evidence for the mode entanglement of neutrino mass eigenstates in a given flavour eigenstate. Given this mode entanglement, it is pertinent to consider the relation between the oscillation probabilities and other quantum correlations. In this work, we show that all the well-known quantum correlations, such as the Bell's inequality, are directly related to the neutrino oscillation probabilities. The results of the neutrino oscillation experiments, which measure the neutrino survival probability to be less than unity, imply Bell's inequality violation.
International Nuclear Information System (INIS)
Tashiro, Tohru
2009-01-01
A parametric oscillator with damping driven by white noise is studied. The mean square displacement (MSD) in the long-time limit is derived analytically for the case that the static force vanishes, which was not treated in the past work (Tashiro and Morita 2007 Physica A 377 401). The formula is asymptotic but is applicable to a general periodic function. On the basis of this formula, some periodic functions reducing MSD remarkably are proposed
The quantum harmonic oscillator on a circle and a deformed quantum field theory
International Nuclear Information System (INIS)
Rego-Monteiro, M.A.
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
Self-Sustaining Dynamical Nuclear Polarization Oscillations in Quantum Dots
DEFF Research Database (Denmark)
Rudner, Mark Spencer; Levitov, Leonid
2013-01-01
Early experiments on spin-blockaded double quantum dots revealed robust, large-amplitude current oscillations in the presence of a static (dc) source-drain bias. Despite experimental evidence implicating dynamical nuclear polarization, the mechanism has remained a mystery. Here we introduce......) and nuclear spin diffusion, which governs dynamics of the spatial profile of nuclear polarization. The proposed framework naturally explains the differences in phenomenology between vertical and lateral quantum dot structures as well as the extremely long oscillation periods....
Symmetries of the quantum damped harmonic oscillator
International Nuclear Information System (INIS)
Guerrero, J; López-Ruiz, F F; Aldaya, V; Cossío, F
2012-01-01
For the non-conservative Caldirola–Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg–Weyl algebra can be found. The inclusion of the standard time evolution generator (which is not a symmetry) as a symmetry in this algebra, in a unitary manner, requires a non-trivial extension of this basic algebra and hence of the physical system itself. Surprisingly, this extension leads directly to the so-called Bateman dual system, which now includes a new particle acting as an energy reservoir. In addition, the Caldirola–Kanai dissipative system can be retrieved by imposing constraints. The algebra of symmetries of the dual system is presented, as well as a quantization that implies, in particular, a first-order Schrödinger equation. As opposed to other approaches, where it is claimed that the spectrum of the Bateman Hamiltonian is complex and discrete, we obtain that it is real and continuous, with infinite degeneracy in all regimes. (paper)
Conventional and anomalous quantum Rabi oscillations in graphene
International Nuclear Information System (INIS)
Khan, Enamullah; Kumar, Vipin; Kumar, Upendra; Setlur, Girish S.
2014-01-01
We study the non linear response of graphene in presence of quantum field in two different regimes. Far from resonance, using our new technique asymptotic rotating wave approximation (ARWA), we obtained that the matter field interaction leads to the slow oscillations like conventional Rabi oscillations observed in conventional semiconductors using well known rotating wave approximation (RWA). The Rabi frequency obtained in both the regimes
On quantum harmonic oscillator being subjected to absolute
Indian Academy of Sciences (India)
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing ...
Classical and quantum position-dependent mass harmonic oscillators
International Nuclear Information System (INIS)
Cruz y Cruz, S.; Negro, J.; Nieto, L.M.
2007-01-01
The position-dependent mass oscillator is studied from both, classical and quantum mechanical points of view, in order to discuss the ambiguity on the operator ordering of the kinetic term in the quantum framework. The results are illustrated by some examples of specific mass functions
From kaons to neutrinos: quantum mechanics of particle oscillations
International Nuclear Information System (INIS)
Zralek, M.
1998-01-01
The problem of particle oscillation is considered in a pedagogical and comprehensive way. Examples from K, B and neutrino physics are given. Conceptual difficulties of the traditional approach to particle oscillation are discussed. It is shown how the probability current density and the wave packet treatments of particle oscillations resolve some problems. It is also shown that only full field theoretical approach is free from conceptual difficulties. The possibility of oscillation of particles produced together with kaons or neutrinos is considered in full wave packet quantum mechanics language. Precise definition of the oscillation of particles which recoil against mixed states is given. The general amplitude which describes the oscillation of two particles in the final states is found. Using this EPR-type amplitude the problem of oscillation of particles recoiling against kaons or neutrinos is resolved. The relativistic EPR correlations on distances of the order of coherence lengths are considered. (author)
Quantum synchronization of quantum van der Pol oscillators with trapped ions.
Lee, Tony E; Sadeghpour, H R
2013-12-06
The van der Pol oscillator is the prototypical self-sustained oscillator and has been used to model nonlinear behavior in biological and other classical processes. We investigate how quantum fluctuations affect phase locking of one or many van der Pol oscillators. We find that phase locking is much more robust in the quantum model than in the equivalent classical model. Trapped-ion experiments are ideally suited to simulate van der Pol oscillators in the quantum regime via sideband heating and cooling of motional modes. We provide realistic experimental parameters for 171Yb+ achievable with current technology.
The Rabi Oscillation in Subdynamic System for Quantum Computing
Directory of Open Access Journals (Sweden)
Bi Qiao
2015-01-01
Full Text Available A quantum computation for the Rabi oscillation based on quantum dots in the subdynamic system is presented. The working states of the original Rabi oscillation are transformed to the eigenvectors of subdynamic system. Then the dissipation and decoherence of the system are only shown in the change of the eigenvalues as phase errors since the eigenvectors are fixed. This allows both dissipation and decoherence controlling to be easier by only correcting relevant phase errors. This method can be extended to general quantum computation systems.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Quantum Oscillator in the Thermostat as a Model in the Thermodynamics of Open Quantum Systems
Sukhanov, Aleksander
2005-01-01
The quantum oscillator in the thermostat is considered as the model of an open quantum system. Our analysis will be heavily founded on the use of the Schroedinger generalized uncertainties relations (SUR). Our first aim is to demonstrate that for the quantum oscillator the state of thermal equilibrium belongs to the correlated coherent states (CCS), which imply the saturation of SUR at any temperature. The obtained results open the perspective for the search of some statistical theory, which ...
Using qubits to reveal quantum signatures of an oscillator
Agarwal, Shantanu
In this thesis, we seek to study the qubit-oscillator system with the aim to identify and quantify inherent quantum features of the oscillator. We show that the quantum signatures of the oscillator get imprinted on the dynamics of the joint system. The two key features which we explore are the quantized energy spectrum of the oscillator and the non-classicality of the oscillator's wave function. To investigate the consequences of the oscillator's discrete energy spectrum, we consider the qubit to be coupled to the oscillator through the Rabi Hamiltonian. Recent developments in fabrication technology have opened up the possibility to explore parameter regimes which were conventionally inaccessible. Motivated by these advancements, we investigate in this thesis a parameter space where the qubit frequency is much smaller than the oscillator frequency and the Rabi frequency is allowed to be an appreciable fraction of the bare frequency of the oscillator. We use the adiabatic approximation to understand the dynamics in this quasi-degenerate qubit regime. By deriving a dressed master equation, we systematically investigate the effects of the environment on the system dynamics. We develop a spectroscopic technique, using which one can probe the steady state response of the driven and damped system. The spectroscopic signal clearly reveals the quantized nature of the oscillator's energy spectrum. We extend the adiabatic approximation, earlier developed only for the single qubit case, to a scenario where multiple qubits interact with the oscillator. Using the extended adiabatic approximation, we study the collapse and revival of multi-qubit observables. We develop analytic expressions for the revival signals which are in good agreement with the numerically evaluated results. Within the quantum restriction imposed by Heisenberg's uncertainty principle, the uncertainty in the position and momentum of an oscillator is minimum and shared equally when the oscillator is prepared
Universal quantum entanglement between an oscillator and continuous fields
International Nuclear Information System (INIS)
Miao Haixing; Danilishin, Stefan; Chen Yanbei
2010-01-01
Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field--even when the environmental temperature is high and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes that are ordered by the entanglement strength to better understand the entanglement structure, analogously to the energy spectrum of an atomic system. In particular, we derive the optical mode that is maximally entangled with the mechanical oscillator, which will be useful for future quantum computing and encoding information into mechanical degrees of freedom.
Quantum efficiency and oscillator strength of site-controlled InAs quantum dots
DEFF Research Database (Denmark)
Albert, F.; Stobbe, Søren; Schneider, C.
2010-01-01
We report on time-resolved photoluminescence spectroscopy to determine the oscillator strength (OS) and the quantum efficiency (QE) of site-controlled InAs quantum dots nucleating on patterned nanoholes. These two quantities are determined by measurements on site-controlled quantum dot (SCQD...
Quantum efficiency and oscillator strength of site-controlled InGaAs quantum dots
DEFF Research Database (Denmark)
Albert, F.; Schneider, C.; Stobbe, Søren
2010-01-01
We report on time-resolved photoluminescence spectroscopy to determine the oscillator strength (OS) and the quantum efficiency (QE) of site-controlled In(Ga)As quantum dots nucleating on patterned nanoholes. These two quantities are determined by measurements on site-controlled quantum dot (SCQD...
Distinguishing quantum from classical oscillations in a driven phase qubit
International Nuclear Information System (INIS)
Shevchenko, S N; Omelyanchouk, A N; Zagoskin, A M; Savel'ev, S; Nori, Franco
2008-01-01
Rabi oscillations are coherent transitions in a quantum two-level system under the influence of a resonant drive, with a much lower frequency dependent on the perturbation amplitude. These serve as one of the signatures of quantum coherent evolution in mesoscopic systems. It was shown recently (Groenbech-Jensen N and Cirillo M 2005 Phys. Rev. Lett. 95 067001) that in phase qubits (current-biased Josephson junctions) this effect can be mimicked by classical oscillations arising due to the anharmonicity of the effective potential. Nevertheless, we find qualitative differences between the classical and quantum effects. Firstly, while the quantum Rabi oscillations can be produced by the subharmonics of the resonant frequency ω 10 (multiphoton processes), the classical effect also exists when the system is excited at the overtones, nω 10 . Secondly, the shape of the resonance is, in the classical case, characteristically asymmetric, whereas quantum resonances are described by symmetric Lorentzians. Thirdly, the anharmonicity of the potential results in the negative shift of the resonant frequency in the classical case, in contrast to the positive Bloch-Siegert shift in the quantum case. We show that in the relevant range of parameters these features allow us to distinguish confidently the bona fide Rabi oscillations from their classical Doppelgaenger
David Shoenberg and the beauty of quantum oscillations
Pudalov, V. M.
2011-01-01
The quantum oscillation effect was discovered in Leiden in 1930, by W. J. de Haas and P. M. van Alphen when measuring magnetization, and by L. W. Shubnikov and de Haas when measuring magnetoresistance. Studying single crystals of bismuth, they observed oscillatory variations in the magnetization and magnetoresistance with magnetic field. Shoenberg, whose first research in Cambridge had been on bismuth, found that much stronger oscillations are observed when a bismuth sample is cooled to liquid helium temperature rather than liquid hydrogen, which had been used by de Haas. In 1938 Shoenberg went from Cambridge to Moscow to study these oscillations at Kapitza's Institute where liquid helium was available at that time. In 1947, J. Marcus observed similar oscillations in zinc and that persuaded Schoenberg to return to this research. After that, the dHvA effect became one of his main research topics. In particular, he developed techniques for quantitative measurement of this effect in many metals. A theoretical explanation of quantum oscillations was given by L. Onsager in 1952, and an analytical quantitative theory by I. M. Lifshitz and A. M. Kosevich in 1955. These theoretical advances seemed to provide a comprehensive description of the effect. Since then, quantum oscillations have been widely used as a tool for measuring Fermi surface extremal cross-sections and all-angle electron scattering times. In his pioneering experiments of the 1960's, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study. It was quite surprising that "magnetic interaction" conditions could cause the apparently weak quantum oscillation effect to have such strong consequences as breaking the sample into magnetic (now called "Shoenberg") domains and forming an inhomogeneous magnetic state. With his contributions to the field of quantum
David Schoenberg and the beauty of quantum oscillations
International Nuclear Information System (INIS)
Pudalov, V.M.
2012-01-01
The quantum oscillation effect was discovered in Leiden, in 1930, by W.J. de Haas and P.M. van Alphen in magnetization measurement, and by L.W. Shubnikov and de Haas - in magnetoresistance. Studying single crystals of bismuth, they observed oscillatory variations of magnetization and magnetoresistance with magnetic field. Shoenberg, whose first research in Cambridge had been on bismuth, found that much stronger oscillations are observed when a bismuth sample is cooled to liquid helium rather than to liquid hydrogen, which had been used by de Haas. In 1938 Shoenberg came from Cambridge to Moscow to study these oscillations at Kapitza Institute where liquid helium was available at that time. In 1947, J. Marcus observed similar oscillations in zinc, that persuaded Shoenberg to return to this research, and, since then, the dHvA effect had been one of his main research topic. In particular, he developed techniques for quantitative measurements of the effect in many metals. Theoretical explanation of quantum oscillations was given by L. Onsager in 1952, and the analytical quantitative theory by I.M. Lifshitz and A.M. Kosevich in 1955. These theoretical advancements seemed to provide a comprehensive description of the effect. Since then, quantum oscillations were commonly considered as a tool for measuring Fermi surface extremal cross-sections and all-angle electron scattering times. However, in his pioneering experiments in 1960s, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study. It was quite unexpected, that under 'magnetic interaction' conditions, the apparently weak effect of quantum oscillations may lead to such strong consequences as breaking the sample into magnetic (now called 'Shoenberg') domains and the formation of an inhomogeneous magnetic state. Owing to his contribution to the field of quantum
An exactly solvable three-dimensional nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A.; Morris, J. R.
2013-01-01
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states
An exactly solvable three-dimensional nonlinear quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
A hydrodynamic formalism for Brownian systems
International Nuclear Information System (INIS)
Pina, E.; Rosales, M.A.
1981-01-01
A formal hydrodynamic approach to Brownian motion is presented and the corresponding equations are derived. Hydrodynamic quantities are expressed in terms of the physical variables characterizing the Brownian systems. Contact is made with the hydrodynamic model of Quantum Mechanics. (author)
Magnetic molecule on a microcantilever: quantum magnetomechanical oscillations.
Jaafar, Reem; Chudnovsky, E M
2009-06-05
We study the quantum dynamics of a system consisting of a magnetic molecule placed on a microcantilever. The amplitude and frequencies of the coupled magnetomechanical oscillations are computed. Parameter-free theory shows that the existing experimental techniques permit observation of the driven coupled oscillations of the spin and the cantilever, as well as of the splitting of the mechanical modes of the cantilever caused by spin tunneling.
Effect of structural disorder on quantum oscillations in graphite
Energy Technology Data Exchange (ETDEWEB)
Camargo, B. C., E-mail: b.c-camargo@yahoo.com.br; Kopelevich, Y. [Instituto de Fisica Gleb Wataghin, Universidade Estadual de Campinas, Unicamp 13083-970, Campinas, São Paulo (Brazil); Usher, A.; Hubbard, S. B. [School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL (United Kingdom)
2016-01-18
We have studied the effect of structural disorder on the de Haas van Alphen and Shubnikov de Haas quantum oscillations measured in natural, Kish, and highly oriented pyrolytic graphite samples at temperatures down to 30 mK and at magnetic fields up to 14 T. The measurements were performed on different samples characterized by means of x-ray diffractometry, transmission electron microscopy, and atomic-force microscopy techniques. Our results reveal a correlation between the amplitude of quantum oscillations and the sample surface roughness.
Classical and quantum properties of optical parametric oscillators
Martinelli, M; Nussenzveig, P; Souto-Ribeiro, P H
2001-01-01
We present a review of the Optical Parametric Oscillator (OPO), describing its operation and the quantum correlation between the light beams generated by this oscillator. We show the construction of an OPO using a Potassium Titanyl Phosphate crystal, pumped by a frequency doubled Nd:YAG laser, and discuss the stability of the system and related thermal effects. We have measured the quantum correlation of signal and idler beams in a transient regime, obtaining a noise correlation level 39 % below the shot noise level.
Classical and quantum properties of optical parametric oscillators
Energy Technology Data Exchange (ETDEWEB)
Martinelli, M.; Alzar, C.L. Garrido; Nussenzveig, P. [Sao Paulo Univ., SP (Brazil); Souto Ribeiro, P.H. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
2001-12-01
We present a review of the Optical Parametric Oscillator (OPO), describing its operation and the quantum correlation between the light beams generated by this oscillator. We show the construction of an OPO using a Potassium Titanyl Phosphate crystal, pumped by a frequency doubled Nd:YAG laser, and discuss the stability of the system and related thermal effects. We have measured the quantum correlation of signal and idler beams in a transient regime, obtaining a noise correlation level 39 % below the shot noise level. (author)
A quantum anharmonic oscillator model for the stock market
Gao, Tingting; Chen, Yu
2017-02-01
A financially interpretable quantum model is proposed to study the probability distributions of the stock price return. The dynamics of a quantum particle is considered an analog of the motion of stock price. Then the probability distributions of price return can be computed from the wave functions that evolve according to Schrodinger equation. Instead of a harmonic oscillator in previous studies, a quantum anharmonic oscillator is applied to the stock in liquid market. The leptokurtic distributions of price return can be reproduced by our quantum model with the introduction of mixed-state and multi-potential. The trend following dominant market, in which the price return follows a bimodal distribution, is discussed as a specific case of the illiquid market.
Quantum dynamics and breakdown of classical realism in nonlinear oscillators
International Nuclear Information System (INIS)
Gat, Omri
2007-01-01
The leading nonclassical term in the quantum dynamics of nonlinear oscillators is calculated in the Moyal quasi-trajectory representation. The irreducibility of the quantum dynamics to phase-space trajectories is quantified by the discrepancy of the canonical quasi-flow and the quasi-flow of a general observable. This discrepancy is shown to imply the breakdown of classical realism that can give rise to a dynamical violation of Bell's inequalities. (fast track communication)
Quantum-classical correspondence for the inverted oscillator
Maamache, Mustapha; Ryeol Choi, Jeong
2017-11-01
While quantum-classical correspondence for a system is a very fundamental problem in modern physics, the understanding of its mechanism is often elusive, so the methods used and the results of detailed theoretical analysis have been accompanied by active debate. In this study, the differences and similarities between quantum and classical behavior for an inverted oscillator have been analyzed based on the description of a complete generalized Airy function-type quantum wave solution. The inverted oscillator model plays an important role in several branches of cosmology and particle physics. The quantum wave packet of the system is composed of many sub-packets that are localized at different positions with regular intervals between them. It is shown from illustrations of the probability density that, although the quantum trajectory of the wave propagation is somewhat different from the corresponding classical one, the difference becomes relatively small when the classical excitation is sufficiently high. We have confirmed that a quantum wave packet moving along a positive or negative direction accelerates over time like a classical wave. From these main interpretations and others in the text, we conclude that our theory exquisitely illustrates quantum and classical correspondence for the system, which is a crucial concept in quantum mechanics. Supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09919503)
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
International Nuclear Information System (INIS)
Chou, Chia-Chun
2016-01-01
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2016-10-15
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Quantum anharmonic oscillator: The airy function approach
Energy Technology Data Exchange (ETDEWEB)
Maiz, F., E-mail: fethimaiz@gmail.com [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia); University of Cartage, Nabeul Engineering Preparatory Institute, Merazka, 8000 Nabeul (Tunisia); AlFaify, S. [King Khalid University, Faculty of Science, Physics Department, PO Box 9004, Abha 61413, Asseer (Saudi Arabia)
2014-05-15
New and simple numerical method is being reported to solve anharmonic oscillator problems. The method is setup to approach the real potential V(x) of the anharmonic oscillator system as a piecewise linear potential u(x) and to solve the Schrödinger equation of the system using the Airy function. Then, solutions continuity conditions lead to the energy quantification condition, and consequently, the energy eigenvalues. For testing purpose, the method was applied on the sextic and octic oscillators systems. The proposed method is found to be realistic, computationally simple, and having high degrees of accuracy. In addition, it can be applied to any form of potential. The results obtained by the proposed method were seen closely agreeing with results reached by other complicated methods.
Surface plasmon quantum cascade lasers as terahertz local oscillators
Hajenius, M.; Khosropanah, P.; Hovenier, J. N.; Gao, J. R.; Klapwijk, T. M.; Barbieri, S.; Dhillon, S.; Filloux, P.; Sirtori, C.; Ritchie, D. A.; Beere, H. E.
2008-01-01
We characterize a heterodyne receiver based on a surface-plasmon waveguide quantum cascade laser (QCL) emitting at 2.84 THz as a local oscillator, and an NbN hot electron bolometer as a mixer. We find that the envelope of the far-field pattern of the QCL is diffraction-limited and superimposed onto
Optimized Binomial Quantum States of Complex Oscillators with Real Spectrum
International Nuclear Information System (INIS)
Zelaya, K D; Rosas-Ortiz, O
2016-01-01
Classical and nonclassical states of quantum complex oscillators with real spectrum are presented. Such states are bi-orthonormal superpositions of n +1 energy eigenvectors of the system with binomial-like coefficients. For large values of n these optimized binomial states behave as photon added coherent states when the imaginary part of the potential is cancelled. (paper)
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...
Revisiting the quantum harmonic oscillator via unilateral Fourier transforms
International Nuclear Information System (INIS)
Nogueira, Pedro H F; Castro, Antonio S de
2016-01-01
The literature on the exponential Fourier approach to the one-dimensional quantum harmonic oscillator problem is revised and criticized. It is shown that the solution of this problem has been built on faulty premises. The problem is revisited via the Fourier sine and cosine transform method and the stationary states are properly determined by requiring definite parity and square-integrable eigenfunctions. (paper)
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
On quantum harmonic oscillator being subjected to absolute potential state. SWAMI NITYAYOGANANDA. Ramakrishna Mission Ashrama, R.K. Beach, Visakhapatnam 530 003, India. E-mail: nityayogananda@gmail.com. MS received 1 May 2015; accepted 6 May 2016; published online 3 December 2016. Abstract.
Coherent Oscillations inside a Quantum Manifold Stabilized by Dissipation
Touzard, S.; Grimm, A.; Leghtas, Z.; Mundhada, S. O.; Reinhold, P.; Axline, C.; Reagor, M.; Chou, K.; Blumoff, J.; Sliwa, K. M.; Shankar, S.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.
2018-04-01
Manipulating the state of a logical quantum bit (qubit) usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schrödinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits.
Coherent Oscillations inside a Quantum Manifold Stabilized by Dissipation
Directory of Open Access Journals (Sweden)
S. Touzard
2018-04-01
Full Text Available Manipulating the state of a logical quantum bit (qubit usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schrödinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits.
Golden quantum oscillator and Binet–Fibonacci calculus
International Nuclear Information System (INIS)
Pashaev, Oktay K; Nalci, Sengul
2012-01-01
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = −1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)
Golden quantum oscillator and Binet-Fibonacci calculus
Energy Technology Data Exchange (ETDEWEB)
Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)
2012-01-13
The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)
International Nuclear Information System (INIS)
Htoon, H.; Shih, C.K.; Takagahara, T.
2003-01-01
We performed extensive studies on quantum decoherence processes of excitons trapped in the various excited states of SAQDs. Energy level structure and dephasing times of excited states were first determined by conducting photoluminescence excitation spectroscopy and wave-packet interferometry on a large number of individual SAQDs. This large statistical basis allows us to extract the correlation between the energy level structure and dephasing times. The major decoherence mechanisms and their active regime were identified from this correlation. A significant suppression of decoherence was also observed in some of the energetically isolated excited states, providing an experimental evidence for the theoretical prediction, known as 'phonon bottleneck effect'. Furthermore, we observed the direct experimental evidence of Rabi oscillation in these excited states with long decoherence times. In addition, a new type of quantum interference (QI) phenomenon was discovered in the wave-packet interferometry experiments performed in the strong excitation regime where the non-linear effects of Rabi oscillation become important. Detailed theoretical investigations attribute this phenomenon to the coherent dynamics resulting from the interplay of Rabi oscillation and QI
Numerical simulation on quantum turbulence created by an oscillating object
Energy Technology Data Exchange (ETDEWEB)
Fujiyama, S; Tsubota, M [Department of Physics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka City, Osaka (Japan)], E-mail: fujiyama@sci.osaka-cu.ac.jp
2009-02-01
We have conducted a numerical simulation of vortex dynamics in superfluid {sup 4}He in the presence of an oscillating sphere. The experiment on a vibrating wire that measured the transition from laminar to turbulent flow is modelled in our simulations. The simulation exhibits the details of vortex growth by the oscillating sphere. Our result also shows that a more realistic modelling may change the destiny of the vortex rings detached from the sphere. We have evaluated the force driven by the sphere in the simulation and have confirmed the onset of the quantum turbulence.
Optical Rabi Oscillations in a Quantum Dot Ensemble
Kujiraoka, Mamiko; Ishi-Hayase, Junko; Akahane, Kouichi; Yamamoto, Naokatsu; Ema, Kazuhiro; Sasaki, Masahide
2010-09-01
We have investigated Rabi oscillations of exciton polarization in a self-assembled InAs quantum dot ensemble. The four-wave mixing signals measured as a function of the average of the pulse area showed the large in-plane anisotropy and nonharmonic oscillations. The experimental results can be well reproduced by a two-level model calculation including three types of inhomogeneities without any fitting parameter. The large anisotropy can be well explained by the anisotropic dipole moments. We also find that the nonharmonic behaviors partly originate from the polarization interference.
Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator
International Nuclear Information System (INIS)
Wang Shao-Hua; Hou Yu-Long; Jing Jian; Wang Qing; Long Zheng-Wen
2014-01-01
The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti—Jaynes—Cummings (AJC) or Jaynes—Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic held) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit. (physics of elementary particles and fields)
Constructive role of Brownian motion: Brownian motors and Stochastic Resonance
Hänggi, Peter
2005-03-01
Noise is usually thought of as the enemy of order rather as a constructive influence. For the phenomena of Stochastic Resonance [1] and Brownian motors [2], however, stochastic noise can play a beneficial role in enhancing detection and/or facilitating directed transmission of information in absence of biasing forces. Brownian motion assisted Stochastic Resonance finds useful applications in physical, technological, biological and biomedical contexts [1,3]. The basic principles that underpin Stochastic Resonance are elucidated and novel applications for nonlinear classical and quantum systems will be addressed. The presence of non-equilibrium disturbances enables to rectify Brownian motion so that quantum and classical objects can be directed around on a priori designed routes in biological and physical systems (Brownian motors). In doing so, the energy from the haphazard motion of (quantum) Brownian particles is extracted to perform useful work against an external load. This very concept together with first experimental realizations are discussed [2,4,5]. [1] L. Gammaitoni, P. Hä'nggi, P. Jung and F. Marchesoni, Stochastic Resonance, Rev. Mod. Phys. 70, 223 (1998).[2] R. D. Astumian and P. Hä'nggi, Brownian motors, Physics Today 55 (11), 33 (2002).[3] P. Hä'nggi, Stochastic Resonace in Physics and Biology, ChemPhysChem 3, 285 (2002).[4] H. Linke, editor, Special Issue on Brownian Motors, Applied Physics A 75, No. 2 (2002).[5] P. Hä'nggi, F. Marchesoni, F. Nori, Brownian motors, Ann. Physik (Leipzig) 14, xxx (2004); cond-mat/0410033.
Coupled Langmuir oscillations in 2-dimensional quantum plasmas
International Nuclear Information System (INIS)
Akbari-Moghanjoughi, M.
2014-01-01
In this work, we present a hydrodynamic model to study the coupled quantum electron plasma oscillations (QEPO) for two dimensional (2D) degenerate plasmas, which incorporates all the essential quantum ingredients such as the statistical degeneracy pressure, electron-exchange, and electron quantum diffraction effect. Effects of diverse physical aspects like the electronic band-dispersion effect, the electron exchange-correlations and the quantum Bohm-potential as well as other important plasma parameters such as the coupling parameter (plasma separation) and the plasma electron number-densities on the linear response of the coupled system are investigated. By studying three different 2D plasma coupling types, namely, graphene-graphene, graphene-metalfilm, and metalfilm-metalfilm coupling configurations, it is remarked that the collective quantum effects can influence the coupled modes quite differently, depending on the type of the plasma configuration. It is also found that the slow and fast QEPO frequency modes respond very differently to the change in plasma parameters. Current findings can help in understanding of the coupled density oscillations in multilayer graphene, graphene-based heterojunctions, or nanofabricated integrated circuits
Time-dependent coupled harmonic oscillators: classical and quantum solutions
International Nuclear Information System (INIS)
Macedo, D.X.; Guedes, I.
2014-01-01
In this work we present the classical and quantum solutions for an arbitrary system of time-dependent coupled harmonic oscillators, where the masses (m), frequencies (ω) and coupling parameter (k) are functions of time. To obtain the classical solutions, we use a coordinate and momentum transformations along with a canonical transformation to write the original Hamiltonian as the sum of two Hamiltonians of uncoupled harmonic oscillators with modified time-dependent frequencies and unitary masses. To obtain the exact quantum solutions we use a unitary transformation and the Lewis and Riesenfeld (LR) invariant method. The exact wave functions are obtained by solving the respective Milne–Pinney (MP) equation for each system. We obtain the solutions for the system with m 1 = m 2 = m 0 e γt , ω 1 = ω 01 e -γt/2 , ω 2 = ω 02 e -γt/2 and k = k 0 . (author)
Entanglement in Quantum Field Theory: particle mixing and oscillations
International Nuclear Information System (INIS)
Blasone, M; Dell'Anno, F; De Siena, S; Illuminati, F
2013-01-01
The phenomena of particle mixing and flavor oscillations in elementary particle physics are associated with multi-mode entanglement of single-particle states. We show that, in the framework of quantum field theory, these phenomena exhibit a fine structure of quantum correlations, as multi-mode multi-particle entanglement appears. Indeed, the presence of anti-particles adds further degrees of freedom, thus providing nontrivial contributions both to flavor entanglement and, more generally, to multi-partite entanglement. By using the global entanglement measure, based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the multiparticle states of two-flavor neutrinos and anti-neutrinos. A direct comparison with the instance of the quantum mechanical Pontecorvo single-particle states is also performed.
Quantum synchronization of a driven self-sustained oscillator.
Walter, Stefan; Nunnenkamp, Andreas; Bruder, Christoph
2014-03-07
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.
Quantum oscillations in insulators with neutral Fermi surfaces
Sodemann, Inti; Chowdhury, Debanjan; Senthil, T.
2018-02-01
We develop a theory of quantum oscillations in insulators with an emergent Fermi sea of neutral fermions minimally coupled to an emergent U(1 ) gauge field. As pointed out by Motrunich [Phys. Rev. B 73, 155115 (2006), 10.1103/PhysRevB.73.155115], in the presence of a physical magnetic field the emergent magnetic field develops a nonzero value leading to Landau quantization for the neutral fermions. We focus on the magnetic field and temperature dependence of the analog of the de Haas-van Alphen effect in two and three dimensions. At temperatures above the effective cyclotron energy, the magnetization oscillations behave similarly to those of an ordinary metal, albeit in a field of a strength that differs from the physical magnetic field. At low temperatures, the oscillations evolve into a series of phase transitions. We provide analytical expressions for the amplitude and period of the oscillations in both of these regimes and simple extrapolations that capture well their crossover. We also describe oscillations in the electrical resistivity of these systems that are expected to be superimposed with the activated temperature behavior characteristic of their insulating nature and discuss suitable experimental conditions for the observation of these effects in mixed-valence insulators and triangular lattice organic materials.
Exact master equation for a noncommutative Brownian particle
International Nuclear Information System (INIS)
Costa Dias, Nuno; Nuno Prata, Joao
2009-01-01
We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale
Rigorous quantum limits on monitoring free masses and harmonic oscillators
Roy, S. M.
2018-03-01
There are heuristic arguments proposing that the accuracy of monitoring position of a free mass m is limited by the standard quantum limit (SQL): σ2( X (t ) ) ≥σ2( X (0 ) ) +(t2/m2) σ2( P (0 ) ) ≥ℏ t /m , where σ2( X (t ) ) and σ2( P (t ) ) denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983), 10.1103/PhysRevLett.51.719] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on σ2( X (t ) ) in terms of σ2( X (0 ) ) and σ2( P (0 ) ) , given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.
Quantum lithography beyond the diffraction limit via Rabi-oscillations
Liao, Zeyang; Al-Amri, Mohammad; Zubairy, M. Suhail
2011-03-01
We propose a quantum optical method to do the sub-wavelength lithography. Our method is similar to the traditional lithography but adding a critical step before dissociating the chemical bound of the photoresist. The subwavelength pattern is achieved by inducing the multi-Rabi-oscillation between the two atomic levels. The proposed method does not require multiphoton absorption and the entanglement of photons. This method is expected to be realizable using current technology. This work is supported by a grant from the Qatar National Research Fund (QNRF) under the NPRP project and a grant from the King Abdulaziz City for Science and Technology (KACST).
Elementary derivation of the quantum propagator for the harmonic oscillator
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Power loss of an oscillating electric dipole in a quantum plasma
Energy Technology Data Exchange (ETDEWEB)
Ghaderipoor, L. [Department of Physics, Faculty of Science, University of Qom, 3716146611 (Iran, Islamic Republic of); Mehramiz, A. [Department of Physics, Faculty of Science, Imam Khomeini Int' l University, Qazvin 34149-16818 (Iran, Islamic Republic of)
2012-12-15
A system of linearized quantum plasma equations (quantum hydrodynamic model) has been used for investigating the dispersion equation for electrostatic waves in the plasma. Furthermore, dispersion relations and their modifications due to quantum effects are used for calculating the power loss of an oscillating electric dipole. Finally, the results are compared in quantum and classical regimes.
Pseudo Landau levels and quantum oscillations in strained Weyl semimetals
Alisultanov, Z. Z.
2018-05-01
The crystal lattice deformation in Weyl materials where the two chiralities are separated in momentum space leads to the appearance of gauge pseudo-fields. We investigated the pseudo-magnetic field induced quantum oscillations in strained Weyl semimetal (WSM). In contrast to all previous works on this problem, we use here a more general tilted Hamiltonian. Such Hamiltonian, seems to be is more suitable for a strained WSMs. We have shown that a pseudo-magnetic field induced magnetization of strained WSM is nonzero due to the fact that electric field (gradient of the deformation potential) is induced simultaneously with the pseudo-magnetic field. This related with fact that the pseudo Landau levels (LLs) in strained WSM are differ in vicinities of different WPs due to the presence of tilt in spectrum. Such violation of the equivalence between Weyl points (WPs) leads to modulation of quantum oscillations. We also showed that magnetization magnitude can be changed by application of an external electric field. In particular, it can be reduced to zero. The possibility of controlling of the magnetization by an electric field is interesting both from a fundamental point of view (a new type of magneto-electric effect) and application point of view (additional possibility to control diamagnetism of deformed WSMs). Finally, a coexistence of type-I and type-II Weyl fermions is possible in the system under investigation. Such phase is absolutely new for physics of topological systems.
Quantum oscillations in quasi-two-dimensional conductors
Galbova, O
2002-01-01
The electronic absorption of sound waves in quasi-two-dimensional conductors in strong magnetic fields, is investigated theoretically. A longitudinal acoustic wave, propagating along the normal n-> to the layer of quasi-two-dimensional conductor (k-> = left brace 0,0,k right brace; u-> = left brace 0,0,u right brace) in magnetic field (B-> = left brace 0, 0, B right brace), is considered. The quasiclassical approach for this geometry is of no interest, due to the absence of interaction between electromagnetic and acoustic waves. The problem is of interest in strong magnetic field when quantization of the charge carriers energy levels takes place. The quantum oscillations in the sound absorption coefficient, as a function of the magnetic field, are theoretically observed. The experimental study of the quantum oscillations in quasi-two-dimensional conductors makes it possible to solve the inverse problem of determining from experimental data the extrema closed sections of the Fermi surface by a plane p sub z = ...
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.
Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J
2012-02-01
Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.
Quantum effects in amplitude death of coupled anharmonic self-oscillators
Amitai, Ehud; Koppenhöfer, Martin; Lörch, Niels; Bruder, Christoph
2018-05-01
Coupling two or more self-oscillating systems may stabilize their zero-amplitude rest state, therefore quenching their oscillation. This phenomenon is termed "amplitude death." Well known and studied in classical self-oscillators, amplitude death was only recently investigated in quantum self-oscillators [Ishibashi and Kanamoto, Phys. Rev. E 96, 052210 (2017), 10.1103/PhysRevE.96.052210]. Quantitative differences between the classical and quantum descriptions were found. Here, we demonstrate that for quantum self-oscillators with anharmonicity in their energy spectrum, multiple resonances in the mean phonon number can be observed. This is a result of the discrete energy spectrum of these oscillators, and is not present in the corresponding classical model. Experiments can be realized with current technology and would demonstrate these genuine quantum effects in the amplitude death phenomenon.
Quantum interference oscillations of the superparamagnetic blocking in an Fe8 molecular nanomagnet
Burzurí, E.; Luis, F.; Montero, O.; Barbara, B.; Ballou, R.; Maegawa, S.
2013-01-01
We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an Fe8 single molecule magnet oscillate as a function of the magnetic field Hx applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by Hx, between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground S=10 and excited multiplets. These experiments enabl...
International Nuclear Information System (INIS)
Sudheer, K. Sebastian; Sabir, M.
2009-01-01
This work investigates function projective synchronization of two-cell Quantum-CNN chaotic oscillators using adaptive method. Quantum-CNN oscillators produce nano scale chaotic oscillations under certain conditions. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.
On the Quantum Potential and Pulsating Wave Packet in the Harmonic Oscillator
International Nuclear Information System (INIS)
Dubois, Daniel M.
2008-01-01
A fundamental mathematical formalism related to the Quantum Potential factor, Q, is presented in this paper. The Schroedinger equation can be transformed to two equations depending on a group velocity and a density of presence of the particle. A factor, in these equations, was called ''Quantum Potential'' by D. Bohm and B. Hiley. In 1999, I demonstrated that this Quantum Potential, Q, can be split in two Quantum Potentials, Q 1 , and Q 2 , for which the relation, Q=Q 1 +Q 2 , holds. These two Quantum Potentials depend on a fundamental new variable, what I called a phase velocity, u, directly related to the probability density of presence of the wave-particle, given by the modulus of the wave function. This paper gives some further developments for explaining the Quantum Potential for oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator. It is shown that the two Quantum Potentials play a central role in the interpretation of quantum mechanics. A breakthrough in the formalism of the Quantum Mechanics could be provoked by the physical properties of these Quantum Potentials. The probability density of presence of the oscillating and pulsating Gaussian wave packets in the Harmonic Oscillator is directly depending on the ratio Q 2 /Q 1 of the two Quantum Potentials. In the general case, the energy of these Gaussian wave packets is not constant, but is oscillating. The energy is given by the sum of the kinetic energy, T, the potential energy, V, and the two Quantum Potentials: E=T+V+Q 1 +Q 2 . For some conditions, given in the paper, the energy can be a constant. The first remarkable result is the fact that the first Quantum Potential, Q 1 , is related to the ground state energy, E 0 , of the Quantum Harmonic Oscillator: Q 1 =h-bar ω/2=E 0 . The second result is related to the property of the second Quantum Potential, Q 2 , which plays the role of an anti-potential, Q 2 =-V(x), where V is the harmonic oscillator potential. This Quantum Potential
Surface plasmon quantum cascade lasers as terahertz local oscillators.
Hajenius, M; Khosropanah, P; Hovenier, J N; Gao, J R; Klapwijk, T M; Barbieri, S; Dhillon, S; Filloux, P; Sirtori, C; Ritchie, D A; Beere, H E
2008-02-15
We characterize a heterodyne receiver based on a surface-plasmon waveguide quantum cascade laser (QCL) emitting at 2.84 THz as a local oscillator, and an NbN hot electron bolometer as a mixer. We find that the envelope of the far-field pattern of the QCL is diffraction-limited and superimposed onto interference fringes, which are similar to those found in narrow double-metal waveguide QCLs. Compared to the latter, a more directional beam allows for better coupling of the radiation power to the mixer. We obtain a receiver noise temperature of 1050 K when the mixer is at 2 K, which, to our knowledge, is the highest sensitivity reported at frequencies beyond 2.5 THz.
Correlation effect of Rabi oscillations of excitons in quantum dots
International Nuclear Information System (INIS)
Ishi-Hayase, J.; Akahane, K.; Yamamoto, Y.; Kujiraoka, M.; Ema, K.; Sasaki, M.
2008-01-01
We performed a transient four-wave mixing experiment on a strain-compensated InAs quantum dot (QD) ensemble over a wide range of excitation intensities. Under the resonant excitation of an exciton ground state, an extremely long dephasing time of 1 ns was found. By increasing the areas of the excitation pulses, Rabi oscillations of excitonic polarizations were clearly observed. The corresponding Rabi frequency is three orders of magnitude higher than the measured dephasing rate. For larger pulse areas, we found that the deviation of experimental data from two-level predictions became significant. The deviations cannot be explained by taking into account, as has been suggested in other research, excitation density-dependent dephasing or Hartree-Fock-type Coulomb interactions between excitons
Quantum oscillator on CPn in a constant magnetic field
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2004-01-01
We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces CP N , as well as on their noncompact counterparts, i.e., the N-dimensional Lobachewski spaces L N . We find the spectrum of this system and the complete basis of wave functions. Surprisingly, the inclusion of a magnetic field does not yield any qualitative change in the energy spectrum. For N>1 the magnetic field does not break the superintegrability of the system, whereas for N=1 it preserves the exact solvability of the system. We extend these results to the cones constructed over CP N and L N , and perform the Kustaanheimo-Stiefel transformation of these systems to the three dimensional Coulomb-like systems
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Bistability and displacement fluctuations in a quantum nanomechanical oscillator
Avriller, R.; Murr, B.; Pistolesi, F.
2018-04-01
Remarkable features have been predicted for the mechanical fluctuations at the bistability transition of a classical oscillator coupled capacitively to a quantum dot [Micchi et al., Phys. Rev. Lett. 115, 206802 (2015), 10.1103/PhysRevLett.115.206802]. These results have been obtained in the regime ℏ ω0≪kBT ≪ℏ Γ , where ω0, T , and Γ are the mechanical resonating frequency, the temperature, and the tunneling rate, respectively. A similar behavior could be expected in the quantum regime of ℏ Γ ≪kBT ≪ℏ ω0 . We thus calculate the energy- and displacement-fluctuation spectra and study their behavior as a function of the electromechanical coupling constant when the system enters the Frank-Condon regime. We find that in analogy with the classical case, the energy-fluctuation spectrum and the displacement spectrum widths show a maximum for values of the coupling constant at which a mechanical bistability is established.
Classical and quantum mechanics of the damped harmonic oscillator
International Nuclear Information System (INIS)
Dekker, H.
1981-01-01
The relations between various treatments of the classical linearly damped harmonic oscillator and its quantization are investigated. In the course of a historical survey typical features of the problem are discussed on the basis of Havas' classical Hamiltonian and the quantum mechanical Suessmann-Hasse-Albrecht models as coined by the Muenchen/Garching nuclear physics group. It is then shown how by imposing a restriction on the classical trajectories in order to connect the Hamiltonian with the energy, the time-independent Bateman-Morse-Feshbach-Bopp Hamiltonian leads to the time-dependent Caldirola-Kanai Hamiltonian. Canonical quantization of either formulation entails a violation of Heisenberg's principle. By means of a unified treatment of both the electrical and mechanical semi-infinite transmission line, this defect is related to the disregard of additional quantum fluctuations that are intrinsically connected with the dissipation. The difficulties of these models are discussed. Then it is proved that the Bateman dual Hamiltonian is connected to a recently developed complex symplectic formulation by a simple canonical transformation. (orig.)
Non-equilibrium effects upon the non-Markovian Caldeira-Leggett quantum master equation
International Nuclear Information System (INIS)
Bolivar, A.O.
2011-01-01
Highlights: → Classical Brownian motion described by a non-Markovian Fokker-Planck equation. → Quantization process. → Quantum Brownian motion described by a non-Markovian Caldeira-Leggett equation. → A non-equilibrium quantum thermal force is predicted. - Abstract: We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker-Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a non-thermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira-Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of a free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.
Quantum enhanced feedback cooling of a mechanical oscillator using nonclassical light.
Schäfermeier, Clemens; Kerdoncuff, Hugo; Hoff, Ulrich B; Fu, Hao; Huck, Alexander; Bilek, Jan; Harris, Glen I; Bowen, Warwick P; Gehring, Tobias; Andersen, Ulrik L
2016-11-29
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics.
Quantum equivalence of a driven triple-well Van der Pol oscillator: A QTM study
International Nuclear Information System (INIS)
Chakraborty, Debdutta; Chattaraj, Pratim Kumar
2014-01-01
Highlights: • Quantum–classical correspondence is manifested at strong external coupling regime. • Suppression of classical chaos takes place in quantum domain. • Quantum chaos promotes quantum diffusion. • Quantum localisation is realised when interference effects are dominant. - Abstract: A quantum mechanical analogue of the classically chaotic triple-well oscillator under the influence of an external field and parametric excitation has been studied by using the quantum theory of motion. The on the fly calculations show the correspondence between some dynamical aspects of the classical and quantum oscillators along with a strictly quantum mechanical behaviour in case of diffusion and tunneling. Suitable external conditions have been obtained which can either assist or suppress the movement of quantum particles from one well to another. Quantum interference effects play a critical role in determining the nature of the quantum dynamics and in the presence of strong coupling to the external forces, quantum interference effects reduce drastically leading to decoherence of the quantum wave packet. In such situations, quantum dynamical features qualitatively resemble the corresponding classical dynamical behaviour and a correspondence between classical and quantum dynamics is obtained
Quantum Transport in Solids: Bloch Dynamics and Role of Oscillating Fields
National Research Council Canada - National Science Library
Kim, Ki
1997-01-01
.... The specific areas of research are those of Bloch electron dynamics, quantum transport in oscillating electric fields or in periodic potentials, and the capacitive nature of atomic size structures...
Quantum damped oscillator II: Bateman's Hamiltonian vs. 2D parabolic potential barrier
International Nuclear Information System (INIS)
Chruscinski, Dariusz
2006-01-01
We show that quantum Bateman's system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba
Non-cyclic phases for neutrino oscillations in quantum field theory
International Nuclear Information System (INIS)
Blasone, Massimo; Capolupo, Antonio; Celeghini, Enrico; Vitiello, Giuseppe
2009-01-01
We show the presence of non-cyclic phases for oscillating neutrinos in the context of quantum field theory. Such phases carry information about the non-perturbative vacuum structure associated with the field mixing. By subtracting the condensate contribution of the flavor vacuum, the previously studied quantum mechanics geometric phase is recovered.
Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations
Muller, A.; Wang, Q. Q.; Bianucci, P.; Xue, Q. K.; Shih, C. K.
2004-01-01
By investigating the polarization-dependent Rabi oscillations using photoluminescence spectroscopy, we determined the respective transition dipole moments of the two excited excitonic states |Ex> and |Ey> of a single self-assembled quantum dot that are nondegenerate due to shape anisotropy. We find that the ratio of the two dipole moments is close to the physical elongation ratio of the quantum dot.
Quantum Interference Oscillations of the Superparamagnetic Blocking in an Fe8 Molecular Nanomagnet
Burzurí, E.; Luis, F.; Montero, O.; Barbara, B.; Ballou, R.; Maegawa, S.
2013-08-01
We show that the dynamic magnetic susceptibility and the superparamagnetic blocking temperature of an Fe8 single molecule magnet oscillate as a function of the magnetic field Hx applied along its hard magnetic axis. These oscillations are associated with quantum interferences, tuned by Hx, between different spin tunneling paths linking two excited magnetic states. The oscillation period is determined by the quantum mixing between the ground S=10 and excited multiplets. These experiments enable us to quantify such mixing. We find that the weight of excited multiplets in the magnetic ground state of Fe8 amounts to approximately 11.6%.
Squeezed light in an optical parametric oscillator network with coherent feedback quantum control.
Crisafulli, Orion; Tezak, Nikolas; Soh, Daniel B S; Armen, Michael A; Mabuchi, Hideo
2013-07-29
We present squeezing and anti-squeezing spectra of the output from a degenerate optical parametric oscillator (OPO) network arranged in different coherent quantum feedback configurations. One OPO serves as a quantum plant, the other as a quantum controller. The addition of coherent feedback enables shaping of the output squeezing spectrum of the plant, and is found to be capable of pushing the frequency of maximum squeezing away from the optical driving frequency and broadening the spectrum over a wider frequency band. The experimental results are in excellent agreement with the developed theory, and illustrate the use of coherent quantum feedback to engineer the quantum-optical properties of the plant OPO output.
Terahertz quantum cascade laser as local oscillator in a heterodyne receiver.
Hübers, Heinz-Wilhelm; Pavlov, S; Semenov, A; Köhler, R; Mahler, L; Tredicucci, A; Beere, H; Ritchie, D; Linfield, E
2005-07-25
Terahertz quantum cascade lasers have been investigated with respect to their performance as a local oscillator in a heterodyne receiver. The beam profile has been measured and transformed in to a close to Gaussian profile resulting in a good matching between the field patterns of the quantum cascade laser and the antenna of a superconducting hot electron bolometric mixer. Noise temperature measurements with the hot electron bolometer and a 2.5 THz quantum cascade laser yielded the same result as with a gas laser as local oscillator.
Determination of anisotropic dipole moments in self-assembled quantum dots using Rabi oscillations
Muller, Andreas; Wang, Qu-Quan; Bianucci, Pablo; Xue, Qi-Kun; Shih, Chih-Kang
2004-03-01
By investigating the polarization-dependent Rabi oscillations using photoluminescence spectroscopy, we determined the respective transition dipole moments of the two excited excitonic states |Ex> and |Ey> of a single self-assembled quantum dot that are nondegenerate due to shape anisotropy. We find that the ratio of the two dipole moments is close to the physical elongation ratio of the quantum dot. We also measured the ground state radiative lifetimes of several quantum dots. The dipole moments calculated from the latter are in reasonable agreement with the dipole moments determined from the periodicity of the Rabi oscillations.
International Nuclear Information System (INIS)
Chung, N. N.; Chew, L. Y.
2007-01-01
We have generalized the two-step approach to the solution of systems of N coupled quantum anharmonic oscillators. By using the squeezed vacuum state of each individual oscillator, we construct the tensor product state, and obtain the optimal squeezed vacuum product state through energy minimization. We then employ this optimal state and its associated bosonic operators to define a basis set to construct the Heisenberg matrix. The diagonalization of the matrix enables us to obtain the energy eigenvalues of the coupled oscillators. In particular, we have applied our formalism to determine the eigenenergies of systems of two coupled quantum anharmonic oscillators perturbed by a general polynomial potential, as well as three and four coupled systems. Furthermore, by performing a first-order perturbation analysis about the optimal squeezed vacuum product state, we have also examined into the squeezing properties of two coupled oscillator systems
Transfer of non-Gaussian quantum states of mechanical oscillator to light
Filip, Radim; Rakhubovsky, Andrey A.
2015-11-01
Non-Gaussian quantum states are key resources for quantum optics with continuous-variable oscillators. The non-Gaussian states can be deterministically prepared by a continuous evolution of the mechanical oscillator isolated in a nonlinear potential. We propose feasible and deterministic transfer of non-Gaussian quantum states of mechanical oscillators to a traveling light beam, using purely all-optical methods. The method relies on only basic feasible and high-quality elements of quantum optics: squeezed states of light, linear optics, homodyne detection, and electro-optical feedforward control of light. By this method, a wide range of novel non-Gaussian states of light can be produced in the future from the mechanical states of levitating particles in optical tweezers, including states necessary for the implementation of an important cubic phase gate.
Quantum resonances in a single plaquette of Josephson junctions: excitations of Rabi oscillations
Fistul, M. V.
2002-03-01
We present a theoretical study of a quantum regime of the resistive (whirling) state of dc driven anisotropic single plaquette containing small Josephson junctions. The current-voltage characteristics of such systems display resonant steps that are due to the resonant interaction between the time dependent Josephson current and the excited electromagnetic oscillations (EOs). The voltage positions of the resonances are determined by the quantum interband transitions of EOs. We show that in the quantum regime as the system is driven on the resonance, coherent Rabi oscillations between the quantum levels of EOs occur. At variance with the classical regime the magnitude and the width of resonances are determined by the frequency of Rabi oscillations that in turn, depends in a peculiar manner on an externally applied magnetic field and the parameters of the system.
International Nuclear Information System (INIS)
Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S.R.
2001-03-01
We discuss the coherent atomic oscillations between two weakly coupled Bose-Einstein condensates. The weak link is provided by a laser barrier in a (possibly asymmetric) double-well trap or by Raman coupling between two condensates in different hyperfine levels. The boson Josephson junction (BJJ) dynamics is described by the two-mode nonlinear Gross-Pitaevskii equation that is solved analytically in terms of elliptic functions. The BJJ, being a neutral, isolated system, allows the investigations of dynamical regimes for the phase difference across the junction and for the population imbalance that are not accessible with superconductor Josephson junctions (SJJ's). These include oscillations with either or both of the following properties: (i) the time-averaged value of the phase is equal to π (π-phase oscillations); (ii) the average population imbalance is nonzero, in states with macroscopic quantum self-trapping. The (nonsinusoidal) generalization of the SJJ ac and plasma oscillations and the Shapiro resonance can also be observed. We predict the collapse of experimental data (corresponding to different trap geometries and the total number of condensate atoms) onto a single universal curve for the inverse period of oscillations. Analogies with Josephson oscillations between two weakly coupled reservoirs of 3 He-B and the internal Josephson effect in 3 He-A are also discussed. (author)
On the moment of inertia of a quantum harmonic oscillator
International Nuclear Information System (INIS)
Khamzin, A. A.; Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-01-01
An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.
Control of entanglement dynamics in a system of three coupled quantum oscillators.
Gonzalez-Henao, J C; Pugliese, E; Euzzor, S; Meucci, R; Roversi, J A; Arecchi, F T
2017-08-30
Dynamical control of entanglement and its connection with the classical concept of instability is an intriguing matter which deserves accurate investigation for its important role in information processing, cryptography and quantum computing. Here we consider a tripartite quantum system made of three coupled quantum parametric oscillators in equilibrium with a common heat bath. The introduced parametrization consists of a pulse train with adjustable amplitude and duty cycle representing a more general case for the perturbation. From the experimental observation of the instability in the classical system we are able to predict the parameter values for which the entangled states exist. A different amount of entanglement and different onset times emerge when comparing two and three quantum oscillators. The system and the parametrization considered here open new perspectives for manipulating quantum features at high temperatures.
International Nuclear Information System (INIS)
Huang Liang; Yang Rui; Lai Yingcheng; Ferry, David K
2013-01-01
Quantum interference causes a wavefunction to have sensitive spatial dependence, and this has a significant effect on quantum transport. For example, in a quantum-dot system, the conductance can depend on the lead positions. We investigate, for graphene quantum dots, the conductance variations with the lead positions. Since for graphene the types of boundaries, e.g., zigzag and armchair, can fundamentally affect the quantum transport characteristics, we focus on rectangular graphene quantum dots, for which the effects of boundaries can be systematically studied. For both zigzag and armchair horizontal boundaries, we find that changing the positions of the leads can induce significant conductance variations. Depending on the Fermi energy, the variations can be either regular oscillations or random conductance fluctuations. We develop a physical theory to elucidate the origin of the conductance oscillation/fluctuation patterns. In particular, quantum interference leads to standing-wave-like-patterns in the quantum dot which, in the absence of leads, are regulated by the energy-band structure of the corresponding vertical graphene ribbon. The observed ‘coexistence’ of regular oscillations and random fluctuations in the conductance can be exploited for the development of graphene-based nanodevices. (paper)
Entanglement entropy in the quantum networks of a coupled quantum harmonic oscillator
International Nuclear Information System (INIS)
Jafarizadeh, M A; Nami, S; Eghbalifam, F
2015-01-01
We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a network are calculated.In partitioning an arbitrary graph into two parts there are some nodes in each part which are not connected to the nodes of the other part. So, these nodes of each part can be in distinct subsets. Therefore, the graph is separated into four subsets. The nodes of the first and last subsets are those which are not connected to the nodes of the other part. In theorem 1, by using the generalized Schur complement method in these four subsets, we prove that all the graphs whose connections between the two alternative subsets are complete, have the same entropy. A large number of graphs satisfy this theorem. Then the entanglement entropy in the limit of the large coupling and large size of the system is investigated in these graphs. Also, the asymptotic behaviors of the Schmidt numbers and entanglement entropy in the limit of infinite coupling are shown.One important quantity about partitioning is the conductance of the graph. The conductance of the graph is considered in various graphs. In these graphs we compare the conductance of the graph and the entanglement entropy. (paper)
Beating of magnetic oscillations in a graphene device probed by quantum capacitance
Tahir, M.; Schwingenschlö gl, Udo
2012-01-01
We report the quantum capacitance of a monolayergraphene device in an external perpendicular magnetic field including the effects of Rashba spin-orbit interaction(SOI). The SOI mixes the spin up and spin down states of neighbouring Landau levels into two (unequally spaced) energy branches. In order to investigate the role of the SOI for the electronic transport, we study the density of states to probe the quantum capacitance of monolayergraphene.SOIeffects on the quantum magnetic oscillations (Shubnikov de Haas and de Hass-van Alphen) are deduced from the quantum capacitance.
Beating of magnetic oscillations in a graphene device probed by quantum capacitance
Tahir, M.
2012-07-05
We report the quantum capacitance of a monolayergraphene device in an external perpendicular magnetic field including the effects of Rashba spin-orbit interaction(SOI). The SOI mixes the spin up and spin down states of neighbouring Landau levels into two (unequally spaced) energy branches. In order to investigate the role of the SOI for the electronic transport, we study the density of states to probe the quantum capacitance of monolayergraphene.SOIeffects on the quantum magnetic oscillations (Shubnikov de Haas and de Hass-van Alphen) are deduced from the quantum capacitance.
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Gordon, Christopher R.
2013-01-01
We analyze the spectral behaviour of a nonlinear quantum oscillator model under confinement. The underlying potential is given by a harmonic oscillator interaction plus a nonlinear term that can be weakened or strengthened through a parameter. Numerical eigenvalues of the model in one and three dimensions are presented. The asymptotic behaviour of the eigenvalues for confinement relaxation and for vanishing nonlinear term in the potential is investigated. Our findings are compared with existing results.
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Quantum damped oscillator II: Bateman’s Hamiltonian vs. 2D parabolic potential barrier
Chruściński, Dariusz
2006-04-01
We show that quantum Bateman’s system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy plane. It is shown that this representation is more suitable than the hyperbolic one used recently by Blasone and Jizba.
Generic mechanisms of decoherence of quantum oscillations in magnetic double-well systems
International Nuclear Information System (INIS)
Chudnovsky, Eugene M.
2004-01-01
Fundamental conservation laws mandate parameter-free generic mechanisms of decoherence of quantum oscillations in double-well systems. We consider two examples: tunneling of the magnetic moment in nanomagnets and tunneling between macroscopic current states in SQUIDs. In both cases the decoherence occurs via emission of phonons and photons at the oscillation frequency. We also show that in a system of identical qubits the decoherence greatly increases due to the superradiance of electromagnetic and sound waves. Our findings have important implications for building elements of quantum computers based upon nanomagnets and SQUIDs
Generic mechanisms of decoherence of quantum oscillations in magnetic double-well systems
Energy Technology Data Exchange (ETDEWEB)
Chudnovsky, Eugene M. E-mail: chudnov@lehman.cuny.edu
2004-05-01
Fundamental conservation laws mandate parameter-free generic mechanisms of decoherence of quantum oscillations in double-well systems. We consider two examples: tunneling of the magnetic moment in nanomagnets and tunneling between macroscopic current states in SQUIDs. In both cases the decoherence occurs via emission of phonons and photons at the oscillation frequency. We also show that in a system of identical qubits the decoherence greatly increases due to the superradiance of electromagnetic and sound waves. Our findings have important implications for building elements of quantum computers based upon nanomagnets and SQUIDs.
Coherent Dynamics of a Hybrid Quantum Spin-Mechanical Oscillator System
Lee, Kenneth William, III
A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantum systems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantum systems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantum systems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface. There are a few important engineering challenges associated with this device. First, there have been no
Dissipation and decoherence in Brownian motion
Energy Technology Data Exchange (ETDEWEB)
Bellomo, Bruno [Dipartimento di Scienze Fisiche ed Astronomiche dell' Universita di Palermo, Via Archirafi, 36, 90123 Palermo (Italy); Barnett, Stephen M [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow G4 0NG (United Kingdom)
2007-05-15
We consider the evolution of a Brownian particle described by a measurement-based master equation. We derive the solution to this equation for general initial conditions and apply it to a Gaussian initial state. We analyse the effects of the diffusive terms, present in the master equation, and describe how these modify uncertainties and coherence length. This allows us to model dissipation and decoherence in quantum Brownian motion.
Area distribution of an elastic Brownian motion
International Nuclear Information System (INIS)
Rajabpour, M A
2009-01-01
We calculate the excursion and meander area distributions of the elastic Brownian motion by using the self-adjoint extension of the Hamiltonian of the free quantum particle on the half line. We also give some comments on the area of the Brownian motion bridge on the real line with the origin removed. We will focus on the power of self-adjoint extension to investigate different possible boundary conditions for the stochastic processes. We also discuss some possible physical applications.
He, Yong
2017-06-23
We utilize the surface plasmon field of a metal nanoparticle (MNP) to show strain-mediated coupling in a quantum dot-mechanical resonator hybrid system including a quantum dot (QD) embedded within a conical nanowire (NW) and a MNP in the presence of an external field. Based on the numerical solutions of the master equation, we find that a slow oscillation, originating from the strain-mediated coupling between the QD and the NW, appears in the time evolution of the plasmon field enhancement. The results show that the period (about [Formula: see text]) of the slow oscillation is equal to that of the mechanical resonator of NW, which suggests that the time-resolved measurement of the plasmon field enhancement can be easily achieved based on the current experimental conditions. Its amplitude increases with the increasing strain-mediated coupling strength, and under certain conditions there is a linear relationship between them. The slow oscillation of the plasmon field enhancement provides valuable tools for measurements of the mechanical frequency and the strain-mediated coupling strength.
Morse oscillator propagator in the high temperature limit II: Quantum dynamics and spectroscopy
Toutounji, Mohamad
2018-04-01
This paper is a continuation of Paper I (Toutounji, 2017) of which motivation was testing the applicability of Morse oscillator propagator whose analytical form was derived by Duru (1983). This is because the Morse oscillator propagator was reported (Duru, 1983) in a triple-integral form of a functional of modified Bessel function of the first kind, which considerably limits its applicability. For this reason, I was prompted to find a regime under which Morse oscillator propagator may be simplified and hence be expressed in a closed-form. This was well accomplished in Paper I. Because Morse oscillator is of central importance and widely used in modelling vibrations, its propagator applicability will be extended to applications in quantum dynamics and spectroscopy as will be reported in this paper using the off-diagonal propagator of Morse oscillator whose analytical form is derived.
Quantum resonances in a single plaquette of Josephson junctions: excitations of Rabi oscillations
Fistul, M. V.
2001-01-01
We present a theoretical study of a quantum regime of the resistive (whirling) state of dc driven anisotropic single plaquette containing three small Josephson junctions. The current-voltage characteristics of such a system display resonant steps that are due to the resonant interaction between the time dependent Josephson current and the excited electromagnetic oscillations (EOs). The voltage positions of the resonances are determined by the quantum interband transitions of EOs. We show that...
Quantum infinite square well with an oscillating wall
International Nuclear Information System (INIS)
Glasser, M.L.; Mateo, J.; Negro, J.; Nieto, L.M.
2009-01-01
A linear matrix equation is considered for determining the time dependent wave function for a particle in a one-dimensional infinite square well having one moving wall. By a truncation approximation, whose validity is checked in the exactly solvable case of a linearly contracting wall, we examine the cases of a simple harmonically oscillating wall and a non-harmonically oscillating wall for which the defining parameters can be varied. For the latter case, we examine in closer detail the dependence on the frequency changes, and we find three regimes: an adiabatic behabiour for low frequencies, a periodic one for high frequencies, and a chaotic behaviour for an intermediate range of frequencies.
López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.
2012-08-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
International Nuclear Information System (INIS)
López-Ruiz, F F; Guerrero, J; Aldaya, V; Cossío, F
2012-01-01
Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.
International Nuclear Information System (INIS)
Luo Jian; Lu Di; Du Chaoling; Liu Youwen; Shi Daning; Lai Wei; Guo Chunlei; Gong Shangqing
2012-01-01
We theoretically investigate how to control the Rabi oscillation of excitons of the coupling quantum dots by manipulating static electric fields. Our results show that, for a single-photon process, when direct excitons change into indirect excitons with a bias applied on the sample, the Rabi oscillation rarely alters. However, for the two-photon process, a pronounced enhancement of Rabi oscillation is observed, which can be utilized as the logic gate in quantum information. (paper)
Quantum theory of damped harmonic oscillator | Antia | Global ...
African Journals Online (AJOL)
The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...
Raby chaotic vacuum oscillations in resonator quantum electrodynamics
International Nuclear Information System (INIS)
Kon'kov, L.E.; Prants, S.V.
1997-01-01
It is shown in numerical experiments with two-level atoms, moving through a single-mode high-quality resonator, that a new type of spontaneous radiation - the Raby chaotic vacuum oscillation - originates in the mode of strong atom-field bonds
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry
Energy Technology Data Exchange (ETDEWEB)
Latini, D., E-mail: latini@fis.uniroma3.it [Department of Mathematics and Physics and INFN, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy); Riglioni, D. [Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, I-00146 Rome (Italy)
2016-10-14
The coalgebraic structure of the harmonic oscillator is used to underline possible connections between continuous and discrete superintegrable models which can be described in terms of SUSY discrete quantum mechanics. A set of 1-parameter algebraic transformations is introduced in order to generate a discrete representation for the coalgebraic harmonic oscillator. This set of transformations is shown to play a role in the generalization of classical orthogonal polynomials to the realm of discrete orthogonal polynomials in the Askey scheme. As an explicit example the connection between Hermite and Charlier oscillators, that share the same coalgebraic structure, is presented and a two-dimensional maximally superintegrable version of the Charlier oscillator is constructed. - Highlights: • We construct a discrete quantum version of the harmonic oscillator. • We solve the spectral problem on the lattice. • We introduce the coalgebra symmetry in real discrete Quantum Mechanics (rdQM). • The coalgebra is used to extend the system to higher dimensions preserving its superintegrability. • We explicitly write down a discrete version of both the angular momentum and the Demkov–Fradkin Tensor.
Rational extension and Jacobi-type Xm solutions of a quantum nonlinear oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, Axel; Roy, Barnana
2013-01-01
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X m exceptional orthogonal polynomials
Rational extension and Jacobi-type X{sub m} solutions of a quantum nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Roy, Barnana [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2013-12-15
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed through Jacobi-type X{sub m} exceptional orthogonal polynomials.
Zhang, Jiayuan
2018-01-01
This article proposes a conception of Brownian coil. Brownian coil is a tiny coil with the same size of pollen. Once immersed into designed magnetic field and liquid, the coil will be moved and deformed macroscopically, due to the microscopic thermodynamic molecular collisions. Such deformation and movement will change the magnetic flux through the coil, by which an ElectroMotive Force (EMF) is produced. In this work, Brownian heat exchanger and Brownian generator are further designed to tran...
Quantum field-theoretical description of neutrino and neutral kaon oscillations
Volobuev, Igor P.
2018-05-01
It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.
There is No Quantum Regression Theorem
International Nuclear Information System (INIS)
Ford, G.W.; OConnell, R.F.
1996-01-01
The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem. copyright 1996 The American Physical Society
Quantum noise of a Michelson-Sagnac interferometer with a translucent mechanical oscillator
International Nuclear Information System (INIS)
Yamamoto, Kazuhiro; Friedrich, Daniel; Westphal, Tobias; Gossler, Stefan; Danzmann, Karsten; Schnabel, Roman; Somiya, Kentaro; Danilishin, Stefan L.
2010-01-01
Quantum fluctuations in the radiation pressure of light can excite stochastic motions of mechanical oscillators thereby realizing a linear quantum opto-mechanical coupling. When performing a precise measurement of the position of an oscillator, this coupling results in quantum radiation pressure noise. Up to now this effect has not been observed yet. Generally speaking, the strength of radiation pressure noise increases when the effective mass of the oscillator is decreased or when the power of the reflected light is increased. Recently, extremely light SiN membranes (≅100 ng) with high mechanical Q values at room temperature (≥10 6 ) have attracted attention as low thermal noise mechanical oscillators. However, the power reflectance of these membranes is much lower than unity (<0.4 at a wavelength of 1064 nm) which makes the use of advanced interferometer recycling techniques to amplify the radiation pressure noise in a standard Michelson interferometer inefficient. Here, we propose and theoretically analyze a Michelson-Sagnac interferometer that includes the membrane as a common end mirror for the Michelson interferometer part. In this topology, both power and signal recycling can be used even if the reflectance of the membrane is much lower than unity. In particular, signal recycling is a useful tool because it does not involve a power increase at the membrane. We derive the formulas for the quantum radiation pressure noise and the shot noise of an oscillator position measurement and compare them with theoretical models of the thermal noise of a SiN membrane with a fundamental resonant frequency of 75 kHz and an effective mass of125 ng. We find that quantum radiation pressure noise should be observable with a power of 1 W at the central beam splitter of the interferometer and a membrane temperature of 1 K.
Filusch, Alexander; Wurl, Christian; Pieper, Andreas; Fehske, Holger
2018-06-01
Simulating quantum transport through mesoscopic, ring-shaped graphene structures, we address various quantum coherence and interference phenomena. First, a perpendicular magnetic field, penetrating the graphene ring, gives rise to Aharonov-Bohm oscillations in the conductance as a function of the magnetic flux, on top of the universal conductance fluctuations. At very high fluxes, the interference gets suppressed and quantum Hall edge channels develop. Second, applying an electrostatic potential to one of the ring arms, nn'n- or npn-junctions can be realized with particle transmission due to normal tunneling or Klein tunneling. In the latter case, the Aharonov-Bohm oscillations weaken for smooth barriers. Third, if potential disorder comes in to play, both Aharonov-Bohm and Klein tunneling effects rate down, up to the point where particle localization sets in.
International Nuclear Information System (INIS)
Sakharov, Alexander; Mavromatos, Nick; Sarkar, Sarben; Meregaglia, Anselmo; Rubbia, Andre
2009-01-01
Quantum gravity may involve models with stochastic fluctuations of the associated metric field, around some fixed background value. Such stochastic models of gravity may induce decoherence for matter propagating in such fluctuating space time. In most cases, this leads to fewer neutrinos of all active flavours being detected in a long baseline experiment as compared to three-flavour standard neutrino oscillations. We discuss the potential of the CNGS and J-PARC beams in constraining models of quantum-gravity induced decoherence using neutrino oscillations as a probe. We use as much as possible model-independent parameterizations, even though they are motivated by specific microscopic models, for fits to the expected experimental data which yield bounds on quantum-gravity decoherence parameters.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... i.e., ρ(θ,q ,p |q,p,t) is a measure of the interference effects associated ... an oscillating electric field, when the initial state is cho- sen as a .... The conclusive effect is that. A±(q,p,t) ...... wave functions ±(q,p,t) stem from the time depen- dence of ..... define a two-dimensional cell in phase space, which is centred ...
Fractional revivals of coherence in quantum mechanical oscillators
Ross, J.C.; Capel, H.W.
2000-01-01
A case study is made of the delocalisation and revival dynamics of a continuously driven quantum pendulum in integrable and near integrable regimes, utilising the Husimi phase-space distribution function, and an entropy function which measures the degree of localisation. The numerical results can be
Quantum oscillations and the electronic transport properties in multichain nanorings
International Nuclear Information System (INIS)
Racolta, D.
2009-01-01
We consider a system of multichain nanorings in static electric and magnetic field. The magnetic field induces characteristic phase changes. These phase shifts produce interference phenomena in the case of nanosystems for which the coherence length is larger than the sample dimension. We obtain energy solutions that are dependent on the number of sites N α characterizing a chain, of phase on the phase φ α and on the applied voltage. We found rich oscillations structures exhibited by the magnetic flux and we established the transmission probability. This proceeds by applying Landauer conductance formulae which opens the way to study electronic transport properties. (authors)
International Nuclear Information System (INIS)
Santos, Marcelo Franca
2005-01-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state
Non-perturbative solution of a quantum mechanical oscillator interacting with a specific environment
International Nuclear Information System (INIS)
Badralexe, E.; Gupta, R.K.; Scheid, W.
1984-01-01
A quantum mechanical model of an oscillator interacting linearly with an environment is treated by the method of perturbation series expansion. For a special class of environments and interactions, the series is summed up to all orders. An integral equation for the time dependence of the coordinate operator of the oscillator is obtained, which is solved analytically by the method of Laplace transformations. General conditions are stated for a dissipative behaviour of the special class of environments considered. An example, which is widely applicable, is discussed. (author)
Synchronisation in coupled quantum Hamiltonian superconducting oscillator via a control potential
International Nuclear Information System (INIS)
Al-Khawaja, Sameer
2009-01-01
This paper presents chaos synchronisation in a SQUID device mutually coupled to a resonant LC classical circuit. Via the Hamiltonian of the coupled quantum-classical system and by means of a 'control potential' in the form of a double-well, measure synchronisation has been found to exist. A transition from quasi-periodic to chaotically synchronised orbits in the phase space has been observed, as the strength of coupling is increased between both oscillators. The system reaches a non-synchronised state if the choice of the control potential were to render both oscillators non-identical.
Advantages of coherent feedback for cooling quantum oscillators.
Hamerly, Ryan; Mabuchi, Hideo
2012-10-26
We model the cooling of open optical and optomechanical resonators via optical feedback in the linear quadratic Gaussian setting of stochastic control theory. We show that coherent feedback control schemes, in which the resonator is embedded in an interferometer to achieve all-optical feedback, can outperform the best possible linear quadratic Gaussian measurement-based schemes in the quantum regime of low steady-state excitation number. Such performance gains are attributed to the coherent controller's ability to process noncommuting output field quadratures simultaneously without loss of fidelity, and may provide important clues for the design of coherent feedback schemes for more general problems of nonlinear and robust control.
Trapped-ion quantum logic gates based on oscillating magnetic fields.
Ospelkaus, C; Langer, C E; Amini, J M; Brown, K R; Leibfried, D; Wineland, D J
2008-08-29
Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.
Quantum perturbation solution of sextic nonlinear oscillator and its classical limit
International Nuclear Information System (INIS)
Jafarpour, M.; Ashrafpour, M.
2000-01-01
We consider the time evolution of the perturbed coherent states to solve the quantum sex tic nonlinear oscillator, in the framework of time dependent perturbation theory. An appropriate limit, h-bar → 0, (absolute value of α)→ ∞,(absolute value of α )√h-bar fixed, is then taken and the classical Poincare'-Landsat series is retrieved. We observe that a proper renormalization of the amplitude and the frequency is needed, if a meaningful comparison between the quantum and the classical results are to be made
Rabi oscillations and quantum beats in a qubit in distorted magnetic field
International Nuclear Information System (INIS)
Ivanchenko, E.A.; Tolstoluzhsky, A.P.
2007-01-01
In a two-level system the time-periodic modulation of the magnetic field stabilizing the magnetic resonance position has been investigated. It was shown that the fundamental resonance is stable with respect to consistent variation of the longitudinal and transverse magnetic fields. The time-dependency of the Rabi oscillations and quantum beats of the spin flip probably was numerically researched in different parameter regimes taking into account dissipation and decoherence in the Lindblad form. The present study may be useful in the analysis of interference experiments and for manipulation of quantum bits
Quantum chaos in the Henon-Heiles oscillator under intense laser fields. IT-1
International Nuclear Information System (INIS)
Gupta, Neetu; Deb, B.M.
2004-01-01
Full text: The quantum domain behaviour of the classically chaotic Henon-Heiles oscillator (HHO) has been studied earlier by several workers, without invoking either a weak or strong time- dependent external perturbation. This work looks at the motion of an electron moving in the HH potential under intense laser fields. The time-dependent Schroedinger equation is numerically solved in order to study the sensitivity of the system to initial conditions. The similarities in responses between the HHO and atoms/molecules to intense laser fields are examined; from this one might speculate that atoms/molecules in intense laser fields might exhibit quantum chaos
Dipolar oscillations in a quantum degenerate Fermi-Bose atomic mixture
International Nuclear Information System (INIS)
Ferlaino, F; Brecha, R J; Hannaford, P; Riboli, F; Roati, G; Modugno, G; Inguscio, M
2003-01-01
We study the dynamics of coupled dipolar oscillations in a Fermi-Bose mixture of 40 K and 87 Rb atoms. This low-energy collective mode is strongly affected by the interspecies interactions. Measurements are performed in the classical and quantum degenerate regimes and reveal the crucial role of the statistical properties of the mixture. At the onset of quantum degeneracy, we investigate the role of Pauli blocking and superfluidity for K and Rb atoms, respectively, resulting in a change in the collisional interactions
Quantum oscillation evidence for a topological semimetal phase in ZrSnTe
Hu, Jin; Zhu, Yanglin; Gui, Xin; Graf, David; Tang, Zhijie; Xie, Weiwei; Mao, Zhiqiang
2018-04-01
The layered WHM-type (W =Zr /Hf /La , H =Si /Ge /Sn /Sb , M =S /Se /Te ) materials represent a large family of topological semimetals, which provides an excellent platform to study the evolution of topological semimetal state with the fine tuning of spin-orbit coupling and structural dimensionality for various combinations of W , H , and M elements. In this work, through high field de Haas-van Alphen (dHvA) quantum oscillation studies, we have found evidence for the predicted topological nontrivial bands in ZrSnTe. Furthermore, from the angular dependence of quantum oscillation frequency, we have revealed the three-dimensional Fermi surface topologies of this layered material owing to strong interlayer coupling.
Energy Technology Data Exchange (ETDEWEB)
Rahmani, S.; Hassanabadi, H. [Shahrood University of Technology, Physics Department, Shahrood (Iran, Islamic Republic of)
2017-09-15
Employing generalized quantum isotonic oscillator potential we determine wave function for mesonic system in nonrelativistic formalism. Then we investigate branching ratios of leptonic decays for heavy-light mesons including a charm quark. Next, by applying the Isgur-Wise function we obtain branching ratios of semileptonic decays for mesons including a bottom quark. The weak decay of the B{sub c} meson is also analyzed to study the life time. Comparison with other available theoretical approaches is presented. (orig.)
Observations of Rabi oscillations in a non-polar InGaN quantum dot
International Nuclear Information System (INIS)
Reid, Benjamin P. L.; Chan, Christopher C. S.; Taylor, Robert A.; Kocher, Claudius; Zhu, Tongtong; Oehler, Fabrice; Emery, Robert; Oliver, Rachel A.
2014-01-01
Experimental observation of Rabi rotations between an exciton excited state and the crystal ground state in a single non-polar InGaN quantum dot is presented. The exciton excited state energy is determined by photoluminescence excitation spectroscopy using two-photon excitation from a pulsed laser. The population of the exciton excited state is seen to undergo power dependent damped Rabi oscillations.
Observations of Rabi oscillations in a non-polar InGaN quantum dot
Energy Technology Data Exchange (ETDEWEB)
Reid, Benjamin P. L., E-mail: benjamin.reid@physics.ox.ac.uk; Chan, Christopher C. S.; Taylor, Robert A. [Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Kocher, Claudius [Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Konstanz University, Konstanz (Germany); Zhu, Tongtong; Oehler, Fabrice; Emery, Robert; Oliver, Rachel A. [Department of Materials Science and Metallurgy, 27 Charles Babbage Road, Cambridge CB3 0FS (United Kingdom)
2014-06-30
Experimental observation of Rabi rotations between an exciton excited state and the crystal ground state in a single non-polar InGaN quantum dot is presented. The exciton excited state energy is determined by photoluminescence excitation spectroscopy using two-photon excitation from a pulsed laser. The population of the exciton excited state is seen to undergo power dependent damped Rabi oscillations.
Quantum oscillation and nontrivial transport in the Dirac semimetal Cd_3As_2 nanodevice
International Nuclear Information System (INIS)
Pan, Haiyang; Wei, Zhongxia; Zhao, Bo; Song, Fengqi; Wang, Baigeng; Zhang, Kang; Gao, Ming; Wang, Xuefeng; Zhang, Rong; Wang, Jue; Han, Min; Pi, Li
2016-01-01
Here, we report on the Shubnikov-de Haas oscillation in high-quality Cd_3As_2 nanowires grown by a chemical vapor deposition approach. The dominant transport of topological Dirac fermions is evident by the nontrivial Berry phase in the Landau Fan diagram. The quantum oscillations rise at a small field of 2 T and preserves up to 100 K, revealing a sizeable Landau level gap and a device mobility of 2138 cm"2" V"−"1" s"−"1. The angle-variable oscillations indicate the isotropy of the bulk Dirac transport. The large estimated mean free path makes the Cd_3As_2 nanowire a promising platform for the one-dimensional transport of Dirac semimetals.
International Nuclear Information System (INIS)
Gudkov, V.V.; Zhevstovskikh, I.V.; Zimbovskaya, N.A.; Okulov, V.I.
1991-01-01
The quantum oscillations are studied of ellipcity, the rotation angle of the ultrasound polarization plane, the velocity and absorption of waves polarized circularly at the 196 MHz frequency in a tungsten single crystal in magnetic field of 30-80 kOe at temperature 1,8 K. The oscillation amplitudes of ellipticity and rotation angle of the ultrasound polarization plane beyond the Doppler-shifted cyclotron resonance are found to vary nonmonotonously with field and to be large enough, so that they are not described by the simple expressions for high fields. The explanation for the oscillation amplification of the polarization parameters is given within the theory involving the ultrasound-spiral wave coupling predicted by Kaner and Skobov. The quantitative comparison in details demonstrates a good agreement in the theory and experimental data and allows to find the numerical values of new parameters characterizing the Fermi surface, electron relaxation frequency, and deformation potential
International Nuclear Information System (INIS)
Wilson, John A
2009-01-01
A detailed exposition is given of recent transport and 'quantum oscillation' results from high temperature superconducting (HTSC) systems covering the full carrier range from overdoped to underdoped material. This now very extensive and high quality data set is here interpreted within the framework developed by the author of local pairs and boson-fermion resonance, arising in the context of negative- U behaviour within an inhomogeneous electronic environment. The strong inhomogeneity comes with the mixed-valence condition of these materials, which when underdoped lie in close proximity to the Mott-Anderson transition. The observed intense scattering is presented as resulting from pair formation and from electron-boson collisions in the resonant crossover circumstance. The high level of scattering carries the systems to incoherence in the pseudogapped state, p c (= 0.183). In a high magnetic field the striped partition of the inhomogeneous charge distribution becomes much strengthened and regularized. Magnetization and resistance oscillations, of period dictated by the favoured positioning of the fluxon array within the real space environment of the diagonal 2D charge striping array, are demonstrated to be responsible for the recently reported behaviour hitherto widely attributed to the quantum oscillation response of a much more standard Fermi liquid condition. A detailed analysis embracing all the experimental data serves to reveal that in the given conditions of very high field, low temperature, 2D-striped, underdoped, d-wave superconducting, HTSC material the flux quantum becomes doubled to h/e.
Quantum oscillation and the Aharonov-Bohm effect in a multiply connected normal-conductor loop
Takai, Daisuke; Ohta, Kuniichi
1994-12-01
The magnetostatic and electrostatic Aharonov-Bohm (AB) effects in multiply connected normal-conductor rings are studied. A previously developed model of a single mesoscopic ring is generalized to include an arbitrary number of rings, and the oscillatory behavior of the total transmission coefficients for the serially connected N (N is equal to integer) rings are derived as a function of the magnetic flux threading each ring and as a function of the electrostatic potential applied to the rings. It is shown that quantum oscillation of multiple rings exhibits greater variety of behavior than in periodic superlattices. We investigate the influence of the scattering at a junction and the number of atoms in the ring in both magnetostatic and electrostatic oscillation of multiring systems. For the electrostatic AB effects, when scattering occurs at the junctions between the connecting wire and the ring, the conductance in the AB oscillation is modified to an N-1 peaked shape. It is shown that this oscillatory behavior is greatly influenced by the number of atoms in the ring and is controlled by the electrostatic potential or magnetic flux that is applied to the ring. We discuss the behavior of the quantum oscillations upon varying the number of connected rings and the number of minibands.
Models with oscillator terms in noncommutative quantum field theory
International Nuclear Information System (INIS)
Kronberger, E.
2010-01-01
The main focus of this Ph.D. thesis is on noncommutative models involving oscillator terms in the action. The first one historically is the successful Grosse-Wulkenhaar (G.W.) model which has already been proven to be renormalizable to all orders of perturbation theory. Remarkably it is furthermore capable of solving the Landau ghost problem. In a first step, we have generalized the G.W. model to gauge theories in a very straightforward way, where the action is BRS invariant and exhibits the good damping properties of the scalar theory by using the same propagator, the so-called Mehler kernel. To be able to handle some more involved one-loop graphs we have programmed a powerful Mathematica package, which is capable of analytically computing Feynman graphs with many terms. The result of those investigations is that new terms originally not present in the action arise, which led us to the conclusion that we should better start from a theory where those terms are already built in. Fortunately there is an action containing this complete set of terms. It can be obtained by coupling a gauge field to the scalar field of the G.W. model, integrating out the latter, and thus 'inducing' a gauge theory. Hence the model is called Induced Gauge Theory. Despite the advantage that it is by construction completely gauge invariant, it contains also some unphysical terms linear in the gauge field. Advantageously we could get rid of these terms using a special gauge dedicated to this purpose. Within this gauge we could again establish the Mehler kernel as gauge field propagator. Furthermore we where able to calculate the ghost propagator, which turned out to be very involved. Thus we were able to start with the first few loop computations showing the expected behavior. The next step is to show renormalizability of the model, where some hints towards this direction will also be given. (author) [de
Brownian modulated optical nanoprobes
International Nuclear Information System (INIS)
Behrend, C.J.; Anker, J.N.; Kopelman, R.
2004-01-01
Brownian modulated optical nanoprobes (Brownian MOONs) are fluorescent micro- and nanoparticles that resemble moons: one hemisphere emits a bright fluorescent signal, while an opaque metal darkens the other hemisphere. Brownian motion causes the particles to tumble and blink erratically as they rotate literally through the phases of the moon. The fluctuating probe signals are separated from optical and electronic backgrounds using principal components analysis or images analysis. Brownian MOONs enable microrheological measurements on size scales and timescales that are difficult to study with other methods. Local chemical concentrations can be measured simultaneously, using spectral characteristics of indicator dyes embedded within the MOONs
Ramsey, Christopher; Del Barco, Enrique; Hill, Stephen; Shah, Sonali; Beedle, Christopher; Hendrickson, David
2008-03-01
The synthetic flexibility of molecular magnets allows one to systematically produce samples with desirable properties such as those with entangled spin states for implementation in quantum logic gates. Here we report direct evidence of quantum oscillations of the total spin length of a dimeric molecular nanomagnet through the observation of quantum interference associated with tunneling trajectories between states having different spin quantum numbers. As we outline, this is a consequence of the unique characteristics of a molecular Mn12 wheel which behaves as a (weak) ferromagnetic exchange-coupled molecular dimer: each half of the molecule acts as a single-molecule magnet (SMM), while the weak coupling between the two halves gives rise to an additional internal spin degree of freedom within the molecule, namely that its total spin may fluctuate. This extra degree of freedom accounts for several magnetization tunneling resonances that cannot be explained within the usual giant spin approximation. More importantly, the observation of quantum interference provides unambiguous evidence for the quantum mechanical superposition involving entangled states of both halves of the wheel.
International Nuclear Information System (INIS)
Arik, M.
1991-01-01
It is shown that the differential calculus of Wess and Zumino for the quantum hyperplane is intimately related to the q-difference operator acting on the n-dimensional complex space C n . An explicit transformation relates the variables and the q-difference operators on C n to the variables and the quantum derivatives on the quantum hyperplane. For real values of the quantum parameter q, the consideration of the variables and the derivatives as hermitean conjugates yields a quantum deformation of the Bargmann-Segal Hilbert space of analytic functions on C n . Physically such a system can be interpreted as the quantum deformation of the n dimensional harmonic oscillator invariant under the unitary quantum group U q (n) with energy eigenvalues proportional to the basic integers. Finally, a construction of the variables and quantum derivatives on the quantum hyperplane in terms of variables and ordinary derivatives on C n is presented. (orig.)
Oscillator strength and quantum-confined Stark effect of excitons in a thin PbS quantum disk
Oukerroum, A.; El-Yadri, M.; El Aouami, A.; Feddi, E.; Dujardin, F.; Duque, C. A.; Sadoqi, M.; Long, G.
2018-01-01
In this paper, we report a study of the effect of a lateral electric field on a quantum-confined exciton in a thin PbS quantum disk. Our approach was performed in the framework of the effective mass theory and adiabatic approximation. The ground state energy and the stark shift were determined by using a variational method with an adequate trial wavefunction, by investigating a 2D oscillator strength under simultaneous consideration of the geometrical confinement and the electric field strength. Our results showed a strong dependence of the exciton binding and the Stark shift on the disk dimensions in both axial and longitudinal directions. On the other hand, our results also showed that the Stark shift’s dependence on the electric field is not purely quadratic but the linear contribution is also important and cannot be neglected, especially when the confinement gets weaker.
Lawler, Gregory F.; Werner, Wendelin
2003-01-01
We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to ``chronologically add Brownian loops'' to simple curves in the plane.
Lin, Z R; Nakamura, Y; Dykman, M I
2015-08-01
We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the difference of the driving amplitude from its critical value. We also find the scaling of the fluctuation correlation time with the quantum noise parameters in the critical region near the threshold. The results are extended to oscillators with nonlinear friction.
O'Connell's process as a vicious Brownian motion
International Nuclear Information System (INIS)
Katori, Makoto
2011-01-01
Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.
Navarrete-Benlloch, Carlos; Roldán, Eugenio; Chang, Yue; Shi, Tao
2014-10-06
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.
Quantum Correlations of Light from a Room-Temperature Mechanical Oscillator
Sudhir, V.; Schilling, R.; Fedorov, S. A.; Schütz, H.; Wilson, D. J.; Kippenberg, T. J.
2017-07-01
When an optical field is reflected from a compliant mirror, its intensity and phase become quantum-correlated due to radiation pressure. These correlations form a valuable resource: the mirror may be viewed as an effective Kerr medium generating squeezed states of light, or the correlations may be used to erase backaction from an interferometric measurement of the mirror's position. To date, optomechanical quantum correlations have been observed in only a handful of cryogenic experiments, owing to the challenge of distilling them from thermomechanical noise. Accessing them at room temperature, however, would significantly extend their practical impact, with applications ranging from gravitational wave detection to chip-scale accelerometry. Here, we observe broadband quantum correlations developed in an optical field due to its interaction with a room-temperature nanomechanical oscillator, taking advantage of its high-cooperativity near-field coupling to an optical microcavity. The correlations manifest as a reduction in the fluctuations of a rotated quadrature of the field, in a frequency window spanning more than an octave below mechanical resonance. This is due to coherent cancellation of the two sources of quantum noise contaminating the measured quadrature—backaction and imprecision. Supplanting the backaction force with an off-resonant test force, we demonstrate the working principle behind a quantum-enhanced "variational" force measurement.
Fermi Surface with Dirac Fermions in CaFeAsF Determined via Quantum Oscillation Measurements
Terashima, Taichi; Hirose, Hishiro T.; Graf, David; Ma, Yonghui; Mu, Gang; Hu, Tao; Suzuki, Katsuhiro; Uji, Shinya; Ikeda, Hiroaki
2018-02-01
Despite the fact that 1111-type iron arsenides hold the record transition temperature of iron-based superconductors, their electronic structures have not been studied much because of the lack of high-quality single crystals. In this study, we comprehensively determine the Fermi surface in the antiferromagnetic state of CaFeAsF, a 1111 iron-arsenide parent compound, by performing quantum oscillation measurements and band-structure calculations. The determined Fermi surface consists of a symmetry-related pair of Dirac electron cylinders and a normal hole cylinder. From analyses of quantum-oscillation phases, we demonstrate that the electron cylinders carry a nontrivial Berry phase π . The carrier density is of the order of 10-3 per Fe. This unusual metallic state with the extremely small carrier density is a consequence of the previously discussed topological feature of the band structure which prevents the antiferromagnetic gap from being a full gap. We also report a nearly linear-in-B magnetoresistance and an anomalous resistivity increase above about 30 T for B ∥c , the latter of which is likely related to the quantum limit of the electron orbit. Intriguingly, the electrical resistivity exhibits a nonmetallic temperature dependence in the paramagnetic tetragonal phase (T >118 K ), which may suggest an incoherent state. Our study provides a detailed knowledge of the Fermi surface in the antiferromagnetic state of 1111 parent compounds and moreover opens up a new possibility to explore Dirac-fermion physics in those compounds.
Manipulation and controlled amplification of Brownian motion of microcantilever sensors
International Nuclear Information System (INIS)
Mehta, Adosh; Cherian, Suman; Hedden, David; Thundat, Thomas
2001-01-01
Microcantilevers, such as those used in atomic force microscopy, undergo Brownian motion due to mechanical thermal noise. The root mean square amplitude of the Brownian motion of a cantilever typically ranges from 0.01--0.1 nm, which limits its use in practical applications. Here we describe a technique by which the Brownian amplitude and the Q factor in air and water can be amplified by three and two orders of magnitude, respectively. This technique is similar to a positive feedback oscillator, wherein the Brownian motion of the vibrating cantilever controls the frequency output of the oscillator. This technique can be exploited to improve sensitivity of microcantilever-based chemical and biological sensors, especially for sensors in liquid environments
Recovery of the Aharonov-Bohm oscillations in asymmetrical quantum rings
Energy Technology Data Exchange (ETDEWEB)
Voskoboynikov, O., E-mail: vam@faculty.nctu.edu.tw [Department of Electronics Engineering, National Chiao Tung University, Hsinchu, Taiwan (China)
2016-07-15
We theoretically investigate suppression and recovery of the Aharonov-Bohm oscillations of the diamagnetic response of electrons (holes) confined in self-assembled In{sub c}Ga{sub 1−c}As/GaAs semiconductor reflection asymmetrical quantum rings. Based on the mapping method and gauge-origin-independent definition for the magnetic vector potential we simulate the energies and wave functions of the electron (hole) under external magnetic and electric fields. We examine the transformation of the ground state wave function of the electron (hole) in reflection asymmetrical rings from localized in one of the potential valleys (dotlike shape of the wave function) to distributed over all volume of the ring (ringlike shape) under an appropriate lateral electric field. This transformation greatly recovers the electron (hole) diamagnetic coefficient and Aharonov-Bohm oscillations of the diamagnetic response of the ring. However, the recovering electric field for the first Aharonov-Bohm diamagnetic oscillation of the electron is a suppressing one for the hole (and vice versa). This can block the recovery of the optical Aharonow-Bohm effect in In{sub c}Ga{sub 1−c}As/GaAs asymmetrically wobbled rings. However, the recovery of the Aharonov-Bohm oscillations for the independent electron (hole) by the external electric field remains interesting and feasible objective for the asymmetric rings.
Reflection Negative Kernels and Fractional Brownian Motion
Directory of Open Access Journals (Sweden)
Palle E. T. Jorgensen
2018-06-01
Full Text Available In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E .
International Nuclear Information System (INIS)
Sebastian, Suchitra E; Gillett, J; Lau, P H C; Lonzarich, G G; Harrison, N; Mielke, C H; Singh, D J
2008-01-01
We report measurements of quantum oscillations in SrFe 2 As 2 -which is an antiferromagnetic parent of the iron arsenide family of superconductors-known to become superconducting under doping and the application of pressure. The magnetic field and temperature dependences of the oscillations between 20 and 55 T in the liquid helium temperature range suggest that the electronic excitations are those of a Fermi liquid. We show that the observed Fermi surface comprising small pockets is consistent with the formation of a spin-density wave. Our measurements thus demonstrate that high T c superconductivity can occur on doping or pressurizing a conventional metallic spin-density wave state. (fast track communication)
Drastic Pressure Effect on the Extremely Large Magnetoresistance in WTe2: Quantum Oscillation Study.
Cai, P L; Hu, J; He, L P; Pan, J; Hong, X C; Zhang, Z; Zhang, J; Wei, J; Mao, Z Q; Li, S Y
2015-07-31
The quantum oscillations of the magnetoresistance under ambient and high pressure have been studied for WTe2 single crystals, in which extremely large magnetoresistance was discovered recently. By analyzing the Shubnikov-de Haas oscillations, four Fermi surfaces are identified, and two of them are found to persist to high pressure. The sizes of these two pockets are comparable, but show increasing difference with pressure. At 0.3 K and in 14.5 T, the magnetoresistance decreases drastically from 1.25×10(5)% under ambient pressure to 7.47×10(3)% under 23.6 kbar, which is likely caused by the relative change of Fermi surfaces. These results support the scenario that the perfect balance between the electron and hole populations is the origin of the extremely large magnetoresistance in WTe2.
The phase of an oscillator in quantum theory. What is it 'in reality'?
International Nuclear Information System (INIS)
Vorontsov, Yurii I
2002-01-01
An analysis of the current theory of the quantum oscillator phase is presented. Predictions using existing approaches to the phase problem differ not only quantitatively but also qualitatively. The question in the title has not yet been given a generally accepted answer. However, it is logical to argue that all the theoretically predicted properties of the phase are physically meaningful if appropriate measurements are possible. Current phase measurement methods either involve the simultaneous (approximate) measurement of the amplitude and the phase or rely on the simultaneous measurement of quadrature amplitudes. (reviews of topical problems)
The phase of an oscillator in quantum theory. What is in reality?
Vorontsov, Y I
2002-01-01
An analysis of the current theory of the quantum oscillator phase is presented. Predictions using existing approaches to the phase problem differ not only quantitatively but also qualitatively. The question in the title has not yet been given a generally accepted answer. However, it is logical to argue that all the theoretically predicted properties of the phase are physically meaningful if appropriate measurements are possible. Current phase measurement methods either involve the simultaneous (approximate) measurement of the amplitude and the phase or rely on the simultaneous measurement of quadrature amplitudes
Exact, E = 0, classical and quantum solutions for general power-law oscillators
International Nuclear Information System (INIS)
Nieto, M.M.; Daboul, J.
1994-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -γ/r ν , γ > 0 and -∞ 0 (t))] 1/μ , with μ = ν/2 - 1 ≠ 0. For ν > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when ν > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed
Modulation response, mixed-mode oscillations and chaotic spiking in quantum dot light emitting diode
International Nuclear Information System (INIS)
Al Husseini, Hussein B.; Al Naimee, Kais A.; Al Khursan, Amin H.; Abdalah, Sora F.; Khedir, Ali H.; Meucci, Riccardo; Arecchi, F. Tito
2015-01-01
In this work quantum dot light emitting diode (QD-LED) was modeled in a dimensionless rate equations system where it is not done earlier. The model was examined first under bias current without any external perturbation where it exhibits chaotic phenomena since the model has multi-degrees of freedom. Then, it is perturbed by both small signal and direct current modulations (DCM), separately. The system exhibits mixed-mode oscillations (MMOs) under DCM. This behavior was reasoned to continuous states of two dimensional wetting layer (WL) which works as a reservoir to quantum dot (QD) states. QD capture was the dominant rate controlling the dynamic behavior in QD-LED. The nonlinear dynamic behavior of our model is compared very well to the experimental observations in the QD-LED
Anisotropic Exciton Rabi Oscillation in Single Telecommunication-Band Quantum Dot
Toshiyuki Miyazawa,; Toshihiro Nakaoka,; Katsuyuki Watanabe,; Naoto Kumagai,; Naoki Yokoyama,; Yasuhiko Arakawa,
2010-06-01
Anisotropic Rabi oscillation in the exciton state in a single InAs/GaAs quantum dot (QD) was demonstrated in the telecommunication-band by selecting two orthogonal polarization angles of the excitation laser. Our InAs QDs were embedded in an intrinsic layer of an n-i-Schottky diode, which provides an electric field to extract photoexcited carriers from QDs. Owing to the potential anisotropy of QDs, the fine structure splitting (FSS) energy in the exciton state in single InAs QDs was ˜110 μeV, measured by polarization-resolved photocurrent spectroscopy. The ratio between two different Rabi frequencies, which reflect anisotropic dipole moments of two orthogonal exciton states, was estimated to be ˜1.2. This demonstrates that the selective control of two orthogonal polarized exciton states is a promising technique for exciton-based-quantum information devices compatible with fiber optics.
Strong Quantum Size Effects in Pb(111) Thin Films Mediated by Anomalous Friedel Oscillations
Jia, Yu; Wu, Biao; Li, Chong; Einstein, T. L.; Weitering, H. H.; Zhang, Zhenyu
2010-08-01
Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films. We show that the FOs at the Pb(111) surface decay as 1/x with the distance x from the surface, different from the conventional 1/x2 power law at other metal surfaces. The underlying physical reason for this striking difference is tied to the strong nesting of the two different Fermi sheets along the Pb(111) direction. The interference of the strong FOs emanating from the two surfaces of a Pb(111) film, in turn, not only results in superoscillatory interlayer relaxations around the center of the film, but also determines its stability in the quantum regime. As a simple and generic picture, the present findings also explain why quantum size effects are exceptionally robust in Pb(111) films.
Trapped-ion quantum logic gates based on oscillating magnetic fields
Ospelkaus, Christian; Langer, Christopher E.; Amini, Jason M.; Brown, Kenton R.; Leibfried, Dietrich; Wineland, David J.
2009-05-01
Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing. With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ions and the electrode surface. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering decoherence, a fundamental source of decoherence in laser-mediated gates. A potentially beneficial environment for the implementation of such schemes is a cryogenic ion trap, because small length scale traps with low motional heating rates can be realized. A cryogenic ion trap experiment is currently under construction at NIST.
Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
Finster, Felix; Hainzl, Christian
2010-01-01
We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which satisfies the dominant energy condition and is time-periodic, thus running through an infinite number of contraction and expansion cycles.
Quantum oscillation measurements of β-LuAlB{sub 4}
Energy Technology Data Exchange (ETDEWEB)
Reiss, Pascal; Baglo, Jordan; Chen, Xiaoye; Tan, HongEn; Sutherland, Michael; Grosche, F. Malte [Cavendish Laboratory, University of Cambridge, Cambridge (United Kingdom); Friedemann, Sven [HH Wills Laboratory, University of Bristol, Bristol (United Kingdom); Goh, Swee K. [Chinese University of Hong Kong, Shatin, N.T. (China); Kuga, Kentaro; Nakatsuji, Satoru [Institute for Solid State Physics, University of Tokyo, Kashiwa (Japan); Harima, Hisatomo [Department of Physics, Graduate School of Science, Kobe University, Kobe (Japan)
2016-07-01
The Yb-based heavy fermion superconductor β-YbAlB{sub 4} displays a quantum critical point without tuning by applied pressure, magnetic field, or doping, which has been attributed to an unusual renormalised band structure. Quantum oscillation measurements of the Fermi surface in β-YbAlB{sub 4} have so far proved inconclusive, motivating us to undertake a detailed study of the isostructural reference compound β-LuAlB{sub 4}, which in contrast to the Yb compound is characterised by a filled 4f shell. We present comprehensive results from rotation and mass studies in β-LuAlB{sub 4}, which broadly agree with band structure calculations and display moderate mass enhancements contrasting with the much larger enhancements seen in β-YbAlB{sub 4} - further emphasising the important contribution of f electrons to the itinerant electron physics of β-YbAlB{sub 4}.
Stochastic incompleteness of quantum mechanics
International Nuclear Information System (INIS)
Suppes, P.; Zanotti, M.
1976-01-01
This article brings out in as conceptually clear terms as possible what seems to be a major incompleteness in the probability theory of particles offered by classical quantum mechanics. The exact nature of this incompleteness is illustrated by consideration of some simple quantum-mechanical examples. In addition, these examples are contrasted with the fundamental assumptions of Brownian motion in classical physics on the one hand, and with a controversey of a deecade ago in mathematical physchology. The central claim is that clasical quantum mechanics is radically incomplete in its probabilistic account of the motion of particles. In the last part of the article the time-dependent joint distribution of position and momentum of the linear harmonic oscillator is derived, and it is shown how the apparently physically paradoxical statistical independence of position and momentum has a natural explanation. The explanation is given within the framework of the non-quantum-mechanical stochastic theory constructed for such oscillators. (Auth.)
Coulomb Oscillations in a Gate-Controlled Few-Layer Graphene Quantum Dot.
Song, Yipu; Xiong, Haonan; Jiang, Wentao; Zhang, Hongyi; Xue, Xiao; Ma, Cheng; Ma, Yulin; Sun, Luyan; Wang, Haiyan; Duan, Luming
2016-10-12
Graphene quantum dots could be an ideal host for spin qubits and thus have been extensively investigated based on graphene nanoribbons and etched nanostructures; however, edge and substrate-induced disorders severely limit device functionality. Here, we report the confinement of quantum dots in few-layer graphene with tunable barriers, defined by local strain and electrostatic gating. Transport measurements unambiguously reveal that confinement barriers are formed by inducing a band gap via the electrostatic gating together with local strain induced constriction. Numerical simulations according to the local top-gate geometry confirm the band gap opening by a perpendicular electric field. We investigate the magnetic field dependence of the energy-level spectra in these graphene quantum dots. Experimental results reveal a complex evolution of Coulomb oscillations with the magnetic field, featuring kinks at level crossings. The simulation of energy spectrum shows that the kink features and the magnetic field dependence are consistent with experimental observations, implying the hybridized nature of energy-level spectrum of these graphene quantum dots.
Time-averaged MSD of Brownian motion
Andreanov, Alexei; Grebenkov, Denis
2012-01-01
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we de...
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
Cariñena, José F.; Plyushchay, Mikhail S.
2017-07-01
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.
International Nuclear Information System (INIS)
Khalil, H.M.; Mazzucato, S.; Ardali, S.; Celik, O.; Mutlu, S.; Royall, B.; Tiras, E.; Balkan, N.; Puustinen, J.; Korpijärvi, V.-M.; Guina, M.
2012-01-01
Highlights: ► We studied p-i-n GaInNAs MQW devices as function of temperature and magnetic field. ► Observed oscillations in the sample current–voltage curves at low temperature. ► Shift in oscillation position with magnetic field described by Landau level split. ► Resonant tunnelling and thermionic emission used to describe oscillations. - Abstract: The photoconductivity of p-i-n GaInNAs/GaAs multiple quantum well (MQW) mesa structures is investigated. When illuminated with photons at energy greater than the GaAs bandgap, a number of oscillations are observed in the current–voltage I–V characteristics. The amplitude and position of the oscillations is shown to depend upon the temperature, as well as upon the exciting wavelength and intensity. Due to the absence of the oscillations in the dark I–V and at temperatures above T = 200 K, we explain them in terms of photogenerated electrons escaping from quantum wells via tunnelling or thermionic emission. Magnetic fields up to B = 11 T were applied parallel to the planes of the QWs. A small voltage shift in the position of the oscillations was observed, proportional to the magnetic field intensity and dependent upon the temperature. Calculation of the Landau level energy separation (16 meV) agrees with the observed experimental data. Magneto-tunnelling spectroscopy probes in detail the nature of band- or impurity-like states responsible for resonances in first and second subbands, observing the I–V plot in dark condition and under illumination. The field-dependence of the amplitude of the oscillation peaks in I–V has the characteristic form of a quantum mechanical admixing effect. This enhancement is also probably due to the hole recombination with majority electrons tunnelling in the N-related states of the quantum wells.
Energy Technology Data Exchange (ETDEWEB)
Khalil, H.M., E-mail: hkhalia@essex.ac.uk [School of Computer Science and Electronic Engineering, University of Essex, CO4 3SQ, Colchester (United Kingdom); Mazzucato, S. [School of Computer Science and Electronic Engineering, University of Essex, CO4 3SQ, Colchester (United Kingdom); Ardali, S.; Celik, O.; Mutlu, S. [Anadolu University, Faculty of Science, Department of Physics, Yunus Emre Campus 26470, Eskisehir (Turkey); Royall, B. [School of Computer Science and Electronic Engineering, University of Essex, CO4 3SQ, Colchester (United Kingdom); Tiras, E. [Anadolu University, Faculty of Science, Department of Physics, Yunus Emre Campus 26470, Eskisehir (Turkey); Balkan, N. [School of Computer Science and Electronic Engineering, University of Essex, CO4 3SQ, Colchester (United Kingdom); Puustinen, J.; Korpijaervi, V.-M.; Guina, M. [Optoelectronics Research Centre, Tampere University of Technology, Korkeakoulunkatu 10, FI-33720 Tampere (Finland)
2012-06-05
Highlights: Black-Right-Pointing-Pointer We studied p-i-n GaInNAs MQW devices as function of temperature and magnetic field. Black-Right-Pointing-Pointer Observed oscillations in the sample current-voltage curves at low temperature. Black-Right-Pointing-Pointer Shift in oscillation position with magnetic field described by Landau level split. Black-Right-Pointing-Pointer Resonant tunnelling and thermionic emission used to describe oscillations. - Abstract: The photoconductivity of p-i-n GaInNAs/GaAs multiple quantum well (MQW) mesa structures is investigated. When illuminated with photons at energy greater than the GaAs bandgap, a number of oscillations are observed in the current-voltage I-V characteristics. The amplitude and position of the oscillations is shown to depend upon the temperature, as well as upon the exciting wavelength and intensity. Due to the absence of the oscillations in the dark I-V and at temperatures above T = 200 K, we explain them in terms of photogenerated electrons escaping from quantum wells via tunnelling or thermionic emission. Magnetic fields up to B = 11 T were applied parallel to the planes of the QWs. A small voltage shift in the position of the oscillations was observed, proportional to the magnetic field intensity and dependent upon the temperature. Calculation of the Landau level energy separation (16 meV) agrees with the observed experimental data. Magneto-tunnelling spectroscopy probes in detail the nature of band- or impurity-like states responsible for resonances in first and second subbands, observing the I-V plot in dark condition and under illumination. The field-dependence of the amplitude of the oscillation peaks in I-V has the characteristic form of a quantum mechanical admixing effect. This enhancement is also probably due to the hole recombination with majority electrons tunnelling in the N-related states of the quantum wells.
Fermi Surface with Dirac Fermions in CaFeAsF Determined via Quantum Oscillation Measurements
Directory of Open Access Journals (Sweden)
Taichi Terashima
2018-02-01
Full Text Available Despite the fact that 1111-type iron arsenides hold the record transition temperature of iron-based superconductors, their electronic structures have not been studied much because of the lack of high-quality single crystals. In this study, we comprehensively determine the Fermi surface in the antiferromagnetic state of CaFeAsF, a 1111 iron-arsenide parent compound, by performing quantum oscillation measurements and band-structure calculations. The determined Fermi surface consists of a symmetry-related pair of Dirac electron cylinders and a normal hole cylinder. From analyses of quantum-oscillation phases, we demonstrate that the electron cylinders carry a nontrivial Berry phase π. The carrier density is of the order of 10^{-3} per Fe. This unusual metallic state with the extremely small carrier density is a consequence of the previously discussed topological feature of the band structure which prevents the antiferromagnetic gap from being a full gap. We also report a nearly linear-in-B magnetoresistance and an anomalous resistivity increase above about 30 T for B∥c, the latter of which is likely related to the quantum limit of the electron orbit. Intriguingly, the electrical resistivity exhibits a nonmetallic temperature dependence in the paramagnetic tetragonal phase (T>118 K, which may suggest an incoherent state. Our study provides a detailed knowledge of the Fermi surface in the antiferromagnetic state of 1111 parent compounds and moreover opens up a new possibility to explore Dirac-fermion physics in those compounds.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
International Nuclear Information System (INIS)
Lin Bihong; Chen Jincan; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily
Quantum-mechanical analysis of low-gain free-electron laser oscillators
Fares, H.; Yamada, M.; Chiadroni, E.; Ferrario, M.
2018-05-01
In the previous classical theory of the low-gain free-electron laser (FEL) oscillators, the electron is described as a point-like particle, a delta function in the spatial space. On the other hand, in the previous quantum treatments, the electron is described as a plane wave with a single momentum state, a delta function in the momentum space. In reality, an electron must have statistical uncertainties in the position and momentum domains. Then, the electron is neither a point-like charge nor a plane wave of a single momentum. In this paper, we rephrase the theory of the low-gain FEL where the interacting electron is represented quantum mechanically by a plane wave with a finite spreading length (i.e., a wave packet). Using the concepts of the transformation of reference frames and the statistical quantum mechanics, an expression for the single-pass radiation gain is derived. The spectral broadening of the radiation is expressed in terms of the spreading length of an electron, the relaxation time characterizing the energy spread of electrons, and the interaction time. We introduce a comparison between our results and those obtained in the already known classical analyses where a good agreement between both results is shown. While the correspondence between our results and the classical results are shown, novel insights into the electron dynamics and the interaction mechanism are presented.
Nuclear resonant scattering of synchrotron radiation from nuclei in the Brownian motion
International Nuclear Information System (INIS)
Razdan, Ashok
2003-01-01
The time evolution of the coherent forward scattering of the synchrotron radiation for resonant nuclei in Brownian motion is studied. Apart from target thickness, the appearance of the dynamical beats also depends on 'α' which is the ratio of the harmonic force constant to the damping force constant of harmonic oscillator undergoing Brownian motion
Dynamics of a Brownian particle in a plasma in the long-time limit
International Nuclear Information System (INIS)
Dickman, R.; Varley, R.L.
1981-01-01
The velocity autocorrelation function (VAF) of a Brownian particle in a plasma is calculated in the long-time limit. The Brownian particle VAF exhibits the same qualitative behavior as the electron VAF in a one-component plasma: oscillations at the plasma frequency and decay approx. t -3 sup(/) 2 . (orig.)
International Nuclear Information System (INIS)
Coffey, W T; Kalmykov, Yu P; Titov, S V; Mulligan, B P
2007-01-01
The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(ℎ 4 ) and in the classical limit, ℎ → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived. (fast track communication)
Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism
Vojta, Günter; Vojta, Matthias
Classical and quantum mechanical Toda systems (Toda molecules, Toda lattices, Toda quantum fields) recently found growing interest as nonlinear systems showing solitons and chaos. In this paper the statistical thermodynamics of a system of quantum mechanical Toda oscillators characterized by a potential energy V(q) = Vo cos h q is treated within the Wigner function formalism (phase space formalism of quantum statistics). The partition function is given as a Wigner- Kirkwood series expansion in terms of powers of h2 (semiclassical expansion). The partition function and all thermodynamic functions are written, with considerable exactness, as simple closed expressions containing only the modified Hankel functions Ko and K1 of the purely imaginary argument i with = Vo/kT.Translated AbstractQuantenstatistik des Toda-Oszillators im Formalismus der Wigner-FunktionKlassische und quantenmechanische Toda-Systeme (Toda-Moleküle, Toda-Gitter, Toda-Quantenfelder) haben als nichtlineare Systeme mit Solitonen und Chaos in jüngster Zeit zunehmend an Interesse gewonnen. Wir untersuchen die statistische Thermodynamik eines Systems quantenmechanischer Toda-Oszillatoren, die durch eine potentielle Energie der Form V(q) = Vo cos h q charakterisiert sind, im Formalismus der Wigner-Funktion (Phasenraum-Formalismus der Quantenstatistik). Die Zustandssumme wird als Wigner-Kirkwood-Reihe nach Potenzen von h2 (semiklassische Entwicklung) dargestellt, und aus ihr werden die thermodynamischen Funktionen berechnet. Sämtliche Funktionen sind durch einfache geschlossene Formeln allein mit den modifizierten Hankel-Funktionen Ko und K1 des rein imaginären Arguments i mit = Vo/kT mit großer Genauigkeit darzustellen.
DEFF Research Database (Denmark)
Leistikow, M.D.; Johansen, Jeppe; Kettelarij, A.J.
2009-01-01
We study experimentally time-resolved emission of colloidal CdSe quantum dots in an environment with a controlled local density of states LDOS. The decay rate is measured versus frequency and as a function of distance to a mirror. We observe a linear relation between the decay rate and the LDOS, ...... with the measured radiative rates. Our results are relevant for applications of CdSe quantum dots in spontaneous emission control and cavity quantum electrodynamics.......We study experimentally time-resolved emission of colloidal CdSe quantum dots in an environment with a controlled local density of states LDOS. The decay rate is measured versus frequency and as a function of distance to a mirror. We observe a linear relation between the decay rate and the LDOS......, allowing us to determine the size-dependent quantum efficiency and oscillator strength. We find that the quantum efficiency decreases with increasing emission energy mostly due to an increase in nonradiative decay. We manage to obtain the oscillator strength of the important class of CdSe quantum dots...
Kloosterman, J.L.; Hayton, D.J.; Ren, Y.; Kao, T.Y.; Hovenier, J.N.; Gao, J.R.; Klapwijk, T.M.; Hu, Q.; Walker, C.K.; Reno, J.L.
2013-01-01
We report on a heterodyne receiver designed to observe the astrophysically important neutral atomic oxygen [OI] line at 4.7448?THz. The local oscillator is a third-order distributed feedback quantum cascade laser operating in continuous wave mode at 4.741?THz. A quasi-optical, superconducting NbN
Quantum dot spin-V(E)CSELs: polarization switching and periodic oscillations
Li, Nianqiang; Alexandropoulos, Dimitris; Susanto, Hadi; Henning, Ian; Adams, Michael
2017-09-01
Spin-polarized vertical (external) cavity surface-emitting lasers [Spin-V(E)CSELs] using quantum dot (QD) material for the active region, can display polarization switching between the right- and left-circularly polarized fields via control of the pump polarization. In particular, our previous experimental results have shown that the output polarization ellipticity of the spin-V(E)CSEL emission can exhibit either the same handedness as that of the pump polarization or the opposite, depending on the experimental operating conditions. In this contribution, we use a modified version of the spin-flip model in conjunction with combined time-independent stability analysis and direct time integration. With two representative sets of parameters our simulation results show good agreement with experimental observations. In addition periodic oscillations provide further insight into the dynamic properties of spin-V(E)CSELs.
Quantum oscillations in antiferromagnetic CaFe2As2 on the brink of superconductivity
International Nuclear Information System (INIS)
Harrison, N; McDonald, R D; Mielke, C H; Bauer, E D; Ronning, F; Thompson, J D
2009-01-01
We report quantum oscillation measurements on CaFe 2 As 2 under strong magnetic fields-recently reported to become superconducting under pressures of as little as a kilobar. The largest observed carrier pocket occupies less than 0.05% of the paramagnetic Brillouin zone volume-consistent with Fermi surface reconstruction caused by antiferromagnetism. On comparing several alkaline earth AFe 2 As 2 antiferromagnets (with A = Ca, Sr and Ba), the dependences of the Fermi surface cross-sectional area F α and the effective mass m α * of the primary observed pocket on the antiferromagnetic/structural transition temperature T s are both found to be consistent with the case for quasiparticles in a conventional spin-density wave model. These findings suggest that the recently proposed strain-enhanced superconductivity in these materials occurs within a broadly conventional spin-density wave phase. (fast track communication)
Magneto-optical properties in inhomogeneous quantum dot: The Aharonov-Bohm oscillations effect
Energy Technology Data Exchange (ETDEWEB)
Nasri, Djillali, E-mail: nasri_dj@yahoo.fr [Faculté des Sciences Appliquées, Département de Génie Electrique, Université Ibn-Khaldoun de Tiaret, Zaaroura BP No. 78, Tiaret 14000 (Algeria); Laboratoirede Microphysique et de Nanophysique (LaMiN), Ecole Nationale Polytechnique d' Oran, BP 1523EL M' Naouer, Oran 31000 (Algeria); Bettahar, N. [Faculté des Sciences de la matière, Département de Physique, Université Ibn-Khaldoun de Tiaret, Zaaroura BP No. 78, Tiaret 14000 (Algeria)
2016-11-15
In this study, we investigated theoretically the effect of a magnetic field B on the linear, nonlinear, and total absorption coefficients (ACs) and the refractive index changes (RICs) associated with intersubband transitions in the HgS quantum shell. In the calculations, a diagonalization method was employed within the effective-mass approximation. We find that a three kinds of optical transitions (S–P, P–D and D–F) between the ground state and the first excited state appear, resulting from the oscillation of the ground state with B (Aharonov-Bohm effect). In the other hand, the magnetic field enhances and diminishes their related RICs and ACs intensities respectively for the three kinds of optical transitions, and shifts their peaks towards low energy (blue shift).
Shot noise of charge current in a quantum dot responded by rotating and oscillating magnetic fields
Energy Technology Data Exchange (ETDEWEB)
Zhao, Hong-Kang, E-mail: zhaohonk@yahoo.com; Zou, Wei-Ke [School of Physics, Beijing Institute of Technology, Beijing 100081 (China); Chen, Qiao [Department of Maths and Physics, Hunan Institute of Engineering, Xiangtan 411104 (China)
2014-09-07
We have investigated the shot noise and Fano factor of the dynamic spin-polarized quantum dot under the perturbations of a rotating magnetic field (RMF), and an oscillating magnetic field (OMF) by employing the non-equilibrium Green's function approach. The shot noise is enhanced from sub-Poissonian to super-Poissonian due to the application of RMF and OMF, and it is controlled sensitively by the tilt angle θ of RMF. The magnitude of shot noise increases as the photon energy ℏω of OMF increases, and its valley eventually is reversed to peaks as the photon energy is large enough. Double-peak structure of Fano factor is exhibited as the frequency of OMF increases to cover a large regime. The Zeeman energy μ{sub 0}B{sub 0} acts as an effective gate bias to exhibit resonant behavior, and novel peak emerges associated with the applied OMF.
International Nuclear Information System (INIS)
Bhattacharyya, S; Das, N R
2012-01-01
In this paper, we study the oscillator strength and cross-section for intersubband optical transition in an n-type semiconductor quantum ring of cylindrical symmetry in the presence of an electric field perpendicular to the plane of the ring. The analysis is done considering Kane-type band non-parabolicity of the semiconductor and assuming that the polarization of the incident radiation is along the axis of the ring. The results show that the oscillator strength decreases and the transition energy increases with the electric field. The assumption of a parabolic band leads to an overestimation of the oscillator strength. The effects of the electric field, band non-parabolicity and relaxation time on absorption cross-section for intersubband transition in a semiconductor quantum ring are also shown. (paper)
Energy Technology Data Exchange (ETDEWEB)
Yuce, C [Physics Department, Anadolu University, Eskisehir (Turkey); Kilic, A [Physics Department, Anadolu University, Eskisehir (Turkey); Coruh, A [Physics Department, Sakarya University, Sakarya (Turkey)
2006-07-15
The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wavefunction for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete, and the energy is given as a linear function of the quantum number n.
On the validity of Brownian assumptions in the spin van der Waals model
International Nuclear Information System (INIS)
Oh, Suhk Kun
1985-01-01
A simple Brownian motion theory of the spin van der Waals model, which can be stationary, Markoffian or Gaussian, is studied. By comparing the Brownian motion theory with an exact theory called the generalized Langevin equation theory, the validity of the Brownian assumptions is tested. Thereby, it is shown explicitly how the Markoffian and Gaussian properties are modified in the spin van der Waals model under the influence of quantum fluctuations and long range ordering. (Author)
International Nuclear Information System (INIS)
Ghasemi, A; Hooshmandasl, M R; Tavassoly, M K
2011-01-01
In this paper we calculate the position and momentum space information entropies for the quantum states associated with a particular physical system, i.e. the isotonic oscillator Hamiltonian. We present our results for its ground states, as well as for its excited states. We observe that the lower bound of the sum of the position and momentum entropies expressed by the Beckner, Bialynicki-Birula and Mycielski (BBM) inequality is satisfied. Moreover, there exist eigenstates that exhibit squeezing in the position information entropy. In fact, entropy squeezing, which occurs in position, will be compensated for by an increase in momentum entropy, such that the BBM inequality is guaranteed. To complete our study we investigate the amplitude squeezing in x and p-quadratures corresponding to the eigenstates of the isotonic oscillator and show that amplitude squeezing, again in x, will be revealed as expected, while the Heisenberg uncertainty relationship is also satisfied. Finally, our numerical calculations of the entropy densities will be presented graphically.
Quantum oscillations and nodal pockets from Fermi surface reconstruction in the underdoped cuprates
Harrison, Neil
2012-02-01
Fermiology in the underdoped high Tc cuprates presents us with unique challenges, requiring experimentalists to look deeper into the data than is normally required for clues. Recent measurements of an oscillatory chemical potential affecting the oscillations at high magnetic fields provide a strong indication of a single type of carrier pocket. When considered in conjunction with photoemission and specific heat measurements, a Fermi surface comprised almost entirely of nodal pockets is suggested. The mystery of the Fermi surface is deepened, however, by a near doping-independent Fermi surface cross-sectional area and negative Hall and Seebeck coefficients. We explore ways in which these findings can be reconciled, taking an important hint from the diverging effective mass yielded by quantum oscillations at low dopings. The author wishes to thank Suchitra Sebastian, Moaz Atarawneh, Doug Bonn, Walter Hardy, Ruixing Liang, Charles Mielke and Gilbert Lonzarich who have contributed to this work. The work is supported by the NSF through the NHMFL and by the DOE project ``Science at 100 tesla.''
Freitas, Nahuel; Paz, Juan Pablo
2018-03-01
We analyze the lowest achievable temperature for a mechanical oscillator coupled with a quantum refrigerator composed of a parametrically driven system that is in contact with a bosonic reservoir where the energy is dumped. We show that the cooling of the oscillator (achieved by the resonant transport of its phonon excitations into the environment) is always stopped by a fundamental heating process that is dominant at sufficiently low temperatures. This process can be described as the nonresonant production of excitation pairs. This result is in close analogy with the recent study that showed that pair production is responsible for enforcing the validity of the dynamical version of the third law of thermodynamics [Phys. Rev. E 95, 012146 (2017), 10.1103/PhysRevE.95.012146]. Interestingly, we relate our model to the ones used to describe laser cooling of a single trapped ion reobtaining the correct limiting temperatures for the regimes of resolved and nonresolved sidebands. We show that the limiting temperature for laser cooling is achieved when the cooling transitions induced by the resonant transport of excitations from the motion into the electromagnetic environment is compensated by the heating transitions induced by the creation of phonon-photon pairs.
The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator
International Nuclear Information System (INIS)
King, R C; Palev, T D; Stoilova, N I; Jeugt, J Van der
2003-01-01
The properties of a non-canonical 3D Wigner quantum oscillator, whose position and momentum operators generate the Lie superalgebra sl(1|3), are further investigated. Within each state space W(p), p = 1, 2, ..., the energy E q , q = 0, 1, 2, 3, takes no more than four different values. If the oscillator is in a stationary state ψ q element of W(p) then measurements of the non-commuting Cartesian coordinates of the particle are such that their allowed values are consistent with it being found at a finite number of sites, called 'nests'. These lie on a sphere centred on the origin of fixed, finite radius ρ q . The nests themselves are at the vertices of a rectangular parallelepiped. In the typical cases (p > 2) the number of nests is 8 for q = 0 and 3, and varies from 8 to 24, depending on the state, for q = 1 and 2. The number of nests is less in the atypical cases (p = 1, 2), but it is never less than 2. In certain states in W(2) (respectively in W(1)) the oscillator is 'polarized' so that all the nests lie on a plane (respectively on a line). The particle cannot be localized in any one of the available nests alone since the coordinates do not commute. The probabilities of measuring particular values of the coordinates are discussed. The mean trajectories and the standard deviations of the coordinates and momenta are computed, and conclusions are drawn about uncertainty relations
Discrete space structure of the sl(1 vertical bar 3) Wigner quantum oscillator
International Nuclear Information System (INIS)
King, R.C.; Palev, T.D.; Stoilova, N.I.; Jeugt, J. van der
2002-09-01
The properties of a noncanonical 3D Wigner quantum oscillator, whose position and momentum operators generate the Lie superalgebra sl(1 vertical bar 3), are further investigated. Within each state space W(p), p=1,2,..., the energy E q , q=0,1,2,3, takes no more than 4 different values. If the oscillator is in a stationary state ψ q is an element of W(p) then measurements of the non-commuting Cartesian coordinates of the particle are such that their allowed values are consistent with it being found at a finite number of sites, called 'nests'. These lie on a sphere centered on the origin of fixed, finite radius p q . The nests themselves are at the vertices of a rectangular parallelepiped. In the typical cases (p>2) the number of nests is 8 for q=0 and 3, and varies from 8 to 24, depending on the state, for q=1 and 2. The number of nests is less in the atypical cases (p=1,2), but it is never less than two. In certain states in W(2) (resp. in W(1)) the oscillator is 'polarized' so that all the nests lie on a plane (resp. on a line). The particle cannot be localized in any one of the available nests alone since the coordinates do not commute. The probabilities of measuring particular values of the coordinates are discussed. The mean trajectories and the standard deviations of the coordinates and momenta are computed, and conclusions are drawn about uncertainty relations. The rotational invariance of the system is also discussed. (author)
Ren, S L; Heremans, J J; Gaspe, C K; Vijeyaragunathan, S; Mishima, T D; Santos, M B
2013-10-30
Low-temperature Aharonov-Bohm oscillations in the magnetoresistance of mesoscopic interferometric rings patterned on an InGaAs/InAlAs heterostructure are investigated for their dependence on excitation current and temperature. The rings have an average radius of 650 nm, and a lithographic arm width of 300 nm, yielding pronounced interference oscillations over a wide range of magnetic fields. Apart from a current and temperature dependence, the oscillation amplitude also shows a quasi-periodic modulation with applied magnetic field. The phase coherence length is extracted by analysis of the fundamental and higher Fourier components of the oscillations, and by direct analysis of the amplitude and its dependence on parameters. It is concluded that the Thouless energy forms the measure of excitation energies for quantum decoherence. The amplitude modulation finds an explanation in the effect of the magnetic flux threading the finite width of the interferometer arms.
International Nuclear Information System (INIS)
Arcos-Olalla, Rafael; Reyes, Marco A.; Rosu, Haret C.
2012-01-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator
Wang, Tao; Huang, Peng; Zhou, Yingming; Liu, Weiqi; Zeng, Guihua
2018-01-01
We propose a pilot-multiplexed continuous-variable quantum key distribution (CVQKD) scheme based on a local local oscillator (LLO). Our scheme utilizes time-multiplexing and polarization-multiplexing techniques to dramatically isolate the quantum signal from the pilot, employs two heterodyne detectors to separately detect the signal and the pilot, and adopts a phase compensation method to almost eliminate the multifrequency phase jitter. In order to analyze the performance of our scheme, a general LLO noise model is constructed. Besides the phase noise and the modulation noise, the photon-leakage noise from the reference path and the quantization noise due to the analog-to-digital converter (ADC) are also considered, which are first analyzed in the LLO regime. Under such general noise model, our scheme has a higher key rate and longer secure distance compared with the preexisting LLO schemes. Moreover, we also conduct an experiment to verify our pilot-multiplexed scheme. Results show that it maintains a low level of the phase noise and is expected to obtain a 554-Kbps secure key rate within a 15-km distance under the finite-size effect.
International Nuclear Information System (INIS)
Harrison, N; McDonald, R D
2009-01-01
We propose a quantum oscillation experiment by which the rotation of an underdoped YBa 2 Cu 3 O 6+x sample about two different axes with respect to the orientation of the magnetic field can be used to infer the shape of the in-plane cross-section of corrugated Fermi surface cylinder(s). Deep corrugations in the Fermi surface are expected to give rise to nodes in the quantum oscillation amplitude that depend on the magnitude and orientation of the magnetic induction B. Because the symmetries of electron and hole cylinders within the Brillouin zone are expected to be very different, the topology can provide essential clues as to the broken symmetry responsible for the observed oscillations. The criterion for the applicability of this method to the cuprate superconductors (as well as other layered metals) is that the difference in quantum oscillation frequency 2ΔF between the maximum (belly) and minimum (neck) extremal cross-sections of the corrugated Fermi surface exceeds |B|. (fast track communication)
Irreversible Brownian Heat Engine
Taye, Mesfin Asfaw
2017-10-01
We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine η =1-√{{Tc/Th}} [23]. On the other hand, the maximum power efficiency of the engine approaches η ^{MAX}=1-({Tc/Th})^{1\\over 4}. It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
International Nuclear Information System (INIS)
Kretzschmar, Martin
1999-01-01
When a Penning trap is operated with an additional quadrupole driving field with a frequency that equals a suitable combination (sum or difference) of the frequencies of the fundamental modes of motion (modified cyclotron, magnetron and axial frequency), then a periodic conversion of the participating modes into each other is observed, strongly resembling the Rabi oscillations in a 2-level atom driven by a laser field tuned to the transition frequency. This investigation attempts to understand on a fundamental level how and why the motion of a classical particle in a macroscopic apparatus can be truely analogous to the oscillations of states of quantum mechanical 2-level systems (2-level atom or magnetic resonance). Ion motion in a Penning trap with an additional quadrupole driving field is described in a quantum mechanical frame work. The Heisenberg equations of motion for the creation and annihilation operators of the interacting oscillators have been explicitly solved, the time development operator of the Schroedinger picture has been determined. The driving field provides for two types of intermode interaction: Type I preserves the total number of excitation quanta present in the two interacting modes, the system oscillates between the modes with a frequency corresponding to the Rabi frequency in two-level systems. Type II preserves the difference of the numbers of excitation quanta present in the two interacting modes, it causes the ion motion to become unbounded. The two types of interaction are associated in a natural way with a SU(2) and a SU(1,1) Lie algebra. The three generators of these algebras form a vector operator that we denote as the Bloch vector operator. The Hilbert space decomposes in a natural way into invariant subspaces, finite dimensional in the case of type I interaction (SU(2)-algebra) and infinite dimensional in the case of type II interaction (SU(1,1)-algebra). The physics of the 2-level atom in the laser field can be described in the 2
Energy Technology Data Exchange (ETDEWEB)
Sadeghi, S. M., E-mail: seyed.sadeghi@uah.edu [University of Alabama in Huntsville, Department of Physics and Nano and Mirco Device Center (United States)
2016-02-15
We investigate formation of unique quantum states (metastates) in quantum dot-metallic nanoparticle systems via self-induced coherent dynamics generated by interaction of these systems with a visible and an infrared laser fields. In such metastates, the quantum decoherence rates of the quantum dots can become zero and even negative while they start to rapidly change with time. Under these conditions, the energy dissipation rates and plasmon fields of the nanoparticle systems undergo undamped oscillations with gigahertz frequency, while the amplitudes of both visible and the infrared laser fields are considered to be time-independent. These dynamics also lead to variation of the plasmon absorption of the metallic nanoparticles between high and nearly zero values, forming electromagnetically induced transparency oscillations. We show that under these conditions, the effective transition energies and broadening of the quantum dots undergo oscillatory dynamics, highlighting the unique aspects of the metastates. These results extend the horizon for investigation of light-matter interaction in the presence of zero or negative polarization dephasing rates with strong time dependency.
International Nuclear Information System (INIS)
Demiralp, Metin
2010-01-01
This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.
Time-averaged MSD of Brownian motion
International Nuclear Information System (INIS)
Andreanov, Alexei; Grebenkov, Denis S
2012-01-01
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution
Time-averaged MSD of Brownian motion
Andreanov, Alexei; Grebenkov, Denis S.
2012-07-01
We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution.
Directory of Open Access Journals (Sweden)
Jeong Ryeol Choi
2015-01-01
Full Text Available An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
Eichhorn, R.; Reimann, P.
2004-04-01
We consider a Brownian particle whose motion is confined to a ``meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ``donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results.
International Nuclear Information System (INIS)
Eichhorn, R.; Reimann, P.
2004-01-01
We consider a Brownian particle whose motion is confined to a ''meandering'' pathway and which is driven away from thermal equilibrium by an alternating external force. This system exhibits absolute negative mobility, i.e. when an external static force is applied the particle moves in the direction opposite to that force. We reveal the physical mechanism behind this ''donkey-like'' behavior, and derive analytical approximations that are in excellent agreement with numerical results. (author)
International Nuclear Information System (INIS)
Mariz, A.M.; Rio Grande do Norte Univ., Natal; Tsallis, C.
1982-01-01
The quantum single one-dimensional oscillator associated with a potential proportional to /X/ sup(#betta#) (#betta# > 0) is discussed. The exact energy eigenvalues recently established by Turschner are further elaborated and convenient exact as well as asymptotic relations are exhibited. The exact T → 0 and T → infinite specific heat is discussed and numerical results for typical values of #betta# and intermediate temperature are presented. (Author) [pt
Aroche, Raúl Riera; Rosas-Cabrera, Rodrigo Arturo; Burgos, Rodrigo Arturo Rosas; Betancourt-Riera, René; Betancourt-Riera, Ricardo
2017-01-01
The formation of Correlated Electron Pairs Oscillating around the Fermi level in Resonant Quantum States (CEPO-RQS), when a metal is cooled to its critical temperature T=Tc, is studied. The necessary conditions for the existence of CEPO-RQS are analyzed. The participation of electron-electron interaction screened by an electron dielectric constant of the form proposed by Thomas Fermi is considered and a physical meaning for the electron-phonon-electron interaction in the formation of the CEPO...
International Nuclear Information System (INIS)
Shen, J.X.; Ossau, W.; Fischer, F.; Waag, A.; Landwehr, G.
1995-01-01
Oscillations of photoluminescence properties in external magnetic fields are investigated in CdTe modulation doped quantum wells. The oscillatory behaviour of the luminescence intensity, the line width and the g factor is due to many-body effects in the 2-dimensional electron gas. The oscillation of photoluminescence intensity can be easily used as optically detected Shubnikov de Haas effect to determine the electron concentration in quantum wells without contacts. (author)
Energy Technology Data Exchange (ETDEWEB)
Shen, J.X.; Ossau, W.; Fischer, F.; Waag, A.; Landwehr, G. [Physikalisches Institut der Uniwersitaet Wuerzburg, Wuerzburg (Germany)
1995-12-31
Oscillations of photoluminescence properties in external magnetic fields are investigated in CdTe modulation doped quantum wells. The oscillatory behaviour of the luminescence intensity, the line width and the g factor is due to many-body effects in the 2-dimensional electron gas. The oscillation of photoluminescence intensity can be easily used as optically detected Shubnikov de Haas effect to determine the electron concentration in quantum wells without contacts. (author). 5 refs, 3 figs, 1 tab.
Fermi surface of superconducting LaFePO determined by quantum oscillations
Energy Technology Data Exchange (ETDEWEB)
Mcdonald, Ross D [Los Alamos National Laboratory; Coldea, A I [BRISTOL UNIV; Fletcher, J D [BRISTOL UNIV; Carrington, A [BRISTOL UNIV; Bangura, A F [BRISTOL UNIV; Hussey, N E [BRISTOL UNIV; Analytis, J G [STANFORD UNIV; Chu, J-h [STANFORD UNIV; Erickson, A S [STANFORD UNIV; Fisher, I R [STANFORD UNIV
2008-01-01
The recent discovery of superconductivity in ferrooxypnictides, which have a maximum transition temperature intermediate between the two other known high temperature superconductors MgB{sub 2} and the cuprate family, has generated huge interest and excitement. The most critical issue is the origin of the pairing mechanism. Whereas superconductivity in MgB{sub 2} has been shown to arise from strong electron-phonon coupling, the pairing glue in cuprate superconductors is thought by many to have a magnetic origin. The oxypnictides are highly susceptible to magnetic instabilities, prompting analogies with cuprate superconductivity. Progress on formulating the correct theory of superconductivity in these materials will be greatly aided by a detailed knowledge of the Fermi surface parameters. Here we report for the first time extensive measurements of quantum oscillations in a Fe-based superconductor, LaFePO, that provide a precise calliper of the size and shape of the Fermi surface and the effective masses of the relevant charge carriers. Our results show that the Fermi surface is composed of nearly-nested electron and hole pockets in broad agreement with the band-structure predictions but with significant enhancement of the quasiparticle masses. The correspondence in the electron and hole Fermi surface areas provides firm experimental evidence that LaFePO, whilst unreconstructed, lies extremely close to a spin-density-wave instability, thus favoring models that invoke such a magnetic origin for high-temperature superconductivity in oxypnictides.
Angle-dependent magnetoresistance and quantum oscillations in high-mobility semimetal LuPtBi
Xu, Guizhou; Hou, Zhipeng; Wang, Yue; Zhang, Xiaoming; Zhang, Hongwei; Liu, Enke; Xi, X; Xu, Feng; Wu, Guangheng; Zhang, Xixiang; Wang, Wenhong
2017-01-01
The recent discovery of ultrahigh mobility and large positive magnetoresistance in topologically non-trivial Half-Heusler semimetal LuPtBi provides a unique playground for studying exotic physics and significant perspective for device applications. As an fcc-structured electron-hole-compensated semimetal, LuPtBi theoretically exhibits six symmetrically arranged anisotropic electron Fermi pockets and two nearly-spherical hole pockets, offering the opportunity to explore the physics of Fermi surface with a simple angle-related magnetotransport properties. In this work, through the angle-dependent transverse magnetoresistance measurements, in combination with high-field SdH quantum oscillations, we achieved to map out a Fermi surface with six anisotropic pockets in the high-temperature and low-field regime, and furthermore, identify a possible magnetic field driven Fermi surface change at lower temperatures. Reasons account for the Fermi surface change in LuPtBi are discussed in terms of the field-induced electron evacuation due to Landau quantization.
Quantum theory of anharmonic oscillators - a variational and systematic general approximation method
International Nuclear Information System (INIS)
Yamazaki, K.; Kyoto Univ.
1984-01-01
The paper investigates the energy levels and wavefunctions of an anharmonic oscillator characterised by the potential 1/2ω 2 q 2 +lambdaq 4 . As a lowest-order approximation an extremely simple formula for energy levels, Esub(i)sup(0) = (i+1/2)1/4(3/αsub(i)+αsub(i)), is derived (i being the quantum number of the energy level). This formula reproduces the exact energy levels within an error of about 1%. Systematically higher orders of the present perturbation theory are developed. The present second-order perturbation theory reduces the errors of the lowest-order results by a factor of about 1/5 in general. Various ranges (large, intermediate, small) of (i, lambda) are investigated and compared with the exact values obtained by other workers. For i = 0, 1, even the fourth-order perturbation calculation can be elaborated explicitly, which reduces the error to about 0.01% for any lambda. For small lambda it gives correct numerical coefficients up to lambda 4 terms, as it should. (author)
Eisfeld, Alexander; Ritschel, Gerhard; Roden, Jan; Strunz, Walter; Aspuru-Guzik, Alan
2012-02-01
Energy transfer in the photosynthetic Fenna-Matthews-Olson (FMO) complex of the Green Sulfur Bacteria is studied theoretically taking all three subunits (monomers) of the FMO trimer and the recently found eighth bacteriochlorophyll (BChl) molecule into account. For the calculations we use the efficient Non-Markovian Quantum State diffusion approach. Since it is believed that the eighth BChl is located near the main light harvesting antenna we look at the differences in transfer between the situation when BChl 8 is initially excited and the usually considered case when BChl 1 or 6 is initially excited. We find strong differences in the transfer dynamics, both qualitatively and quantitatively. When the excited state dynamics is initialized at site eight of the FMO complex, we see a slow exponential-like decay of the excitation. This is in contrast to the oscillations and a relatively fast transfer that occurs when only seven sites or initialization at sites 1 and 6 is considered. Additionally we show that differences in the values of the electronic transition energies found in the literature lead to a large difference in the transfer dynamics.
Angle-dependent magnetoresistance and quantum oscillations in high-mobility semimetal LuPtBi
Xu, Guizhou
2017-03-14
The recent discovery of ultrahigh mobility and large positive magnetoresistance in topologically non-trivial Half-Heusler semimetal LuPtBi provides a unique playground for studying exotic physics and significant perspective for device applications. As an fcc-structured electron-hole-compensated semimetal, LuPtBi theoretically exhibits six symmetrically arranged anisotropic electron Fermi pockets and two nearly-spherical hole pockets, offering the opportunity to explore the physics of Fermi surface with a simple angle-related magnetotransport properties. In this work, through the angle-dependent transverse magnetoresistance measurements, in combination with high-field SdH quantum oscillations, we achieved to map out a Fermi surface with six anisotropic pockets in the high-temperature and low-field regime, and furthermore, identify a possible magnetic field driven Fermi surface change at lower temperatures. Reasons account for the Fermi surface change in LuPtBi are discussed in terms of the field-induced electron evacuation due to Landau quantization.
Energy Technology Data Exchange (ETDEWEB)
Rogacheva, E. I.; Budnik, A. V.; Sipatov, A. Yu.; Nashchekina, O. N. [National Technical University “Kharkov Polytechnic Institute,” 21 Frunze St., Kharkov 61002 (Ukraine); Dresselhaus, M. S. [Department of Electrical Engineering and Computer Science and Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139 (United States)
2015-02-02
The dependences of the electrical conductivity, the Hall coefficient, and the Seebeck coefficient on the layer thickness d (d = 18−600 nm) of p-type topological insulator Bi{sub 2}Te{sub 3} thin films grown by thermal evaporation in vacuum on glass substrates were obtained at room temperature. In the thickness range of d = 18–100 nm, sustained oscillations with a substantial amplitude were revealed. The observed oscillations are well approximated by a harmonic function with a period Δd = (9.5 ± 0.5) nm. At d > 100 nm, the transport coefficients practically do not change as d is increased. The oscillations of the kinetic properties are attributed to the quantum size effects due to the hole confinement in the Bi{sub 2}Te{sub 3} quantum wells. The results of the theoretical calculations of Δd within the framework of a model of an infinitely deep potential well are in good agreement with the experimental results. It is suggested that the substantial amplitude of the oscillations and their sustained character as a function of d are connected with the topologically protected gapless surface states of Bi{sub 2}Te{sub 3} and are inherent to topological insulators.
International Nuclear Information System (INIS)
Kun, S.Yu.; Australian Nat. Univ., Canberra; Australian National Univ., Canberra, ACT
1997-01-01
We employ stochastic modelling of statistical reactions with memory to study quasiperiodic oscillations in the excitation functions of dissipative heavy-ion collisions. The Fourier analysis of excitation function oscillations is presented. It suggests that S-matrix spin and parity decoherence, damping of the coherent nuclear rotation and quantum chaos are sufficient conditions to explain the nonself-averaging of quasiperiodic oscillations in the excitation functions of dissipative heavy-ion collisions. (orig.)
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Ley Koo, E.
The exact solution of the Schrodinger equation for the systems and the boundary condition stated in the title is constructed. The familiar cases of the ordinary harmonic oscillator and the half oscillator are immediately identified. The connection with the double oscillator is also established and is helpful to understand the energy spectrum of the latter. Similar connections can be used to study other partial oscillators. (Author) [pt
Deformation quantization of noncommutative quantum mechanics and dissipation
Energy Technology Data Exchange (ETDEWEB)
Bastos, C [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Dias, N C [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal); Prata, J N [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal)
2007-05-15
We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a *-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.
Exponential energy growth due to slow parameter oscillations in quantum mechanical systems.
Turaev, Dmitry
2016-05-01
It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
On the distribution of estimators of diffusion constants for Brownian motion
International Nuclear Information System (INIS)
Boyer, Denis; Dean, David S
2011-01-01
We discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of quadratic functionals of Brownian motion that correspond to the Euclidean path integral for simple Harmonic oscillators with time dependent frequencies. Explicit analytical results are given for the distribution of the diffusion constant estimator in a number of cases and our results are confirmed by numerical simulations.
Temperature dependence of Coulomb oscillations in a few-layer two-dimensional WS2 quantum dot.
Song, Xiang-Xiang; Zhang, Zhuo-Zhi; You, Jie; Liu, Di; Li, Hai-Ou; Cao, Gang; Xiao, Ming; Guo, Guo-Ping
2015-11-05
Standard semiconductor fabrication techniques are used to fabricate a quantum dot (QD) made of WS2, where Coulomb oscillations were found. The full-width-at-half-maximum of the Coulomb peaks increases linearly with temperature while the height of the peaks remains almost independent of temperature, which is consistent with standard semiconductor QD theory. Unlike graphene etched QDs, where Coulomb peaks belonging to the same QD can have different temperature dependences, these results indicate the absence of the disordered confining potential. This difference in the potential-forming mechanism between graphene etched QDs and WS2 QDs may be the reason for the larger potential fluctuation found in graphene QDs.
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
A model of the two-dimensional quantum harmonic oscillator in an AdS{sub 3} background
Energy Technology Data Exchange (ETDEWEB)
Frick, R. [Universitaet zu Koeln, Institut fuer Theoretische Physik, Cologne (Germany)
2016-10-15
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a three-dimensional anti-de Sitter background. We use a generalized Schroedinger picture in which the analogs of the Schroedinger operators of the particle are independent of both the time and the space coordinates in different representations. The spacetime independent operators of the particle induce the Lie algebra of Killing vector fields of the AdS{sub 3} spacetime. In this picture, we have a metamorphosis of the Heisenberg uncertainty relations. (orig.)
Zhao, K.; Golias, E.; Zhang, Q. H.; Krivenkov, M.; Jesche, A.; Gu, L.; Rader, O.; Mazin, I. I.; Gegenwart, P.
2018-03-01
We have synthesized single crystals of Dirac semimetal candidates A ZnBi2 with A =Ba and Sr. In contrast to A =Sr , the Ba material displays a local Zn vacancy ordering, which makes the observation of quantum oscillations in out-of-plane magnetic fields possible. As a Dirac semimetal candidate, BaZnBi2 exhibits a small cyclotron electron mass, high quantum mobility, and nontrivial Berry phases. Three Dirac dispersions are observed by angle-resolved photoemission spectroscopy and identified by first-principles band-structure calculations. Compared to A Mn(Bi/Sb) 2 systems which host Mn magnetic moments, BaZnBi2 acts as a nonmagnetic analog to investigate the intrinsic properties of Dirac fermions in this structure family.
International Nuclear Information System (INIS)
Gvozdikov, V M; Taut, M
2009-01-01
We report on analytical and numerical studies of the magnetic quantum oscillations of the diagonal conductivity σ xx in a two-dimensional conductor with a weak square superlattice modulation under conditions of the integer quantum Hall (IQHE) effect. The quantum Hall effect in such a system differs from the conventional IQHE, in which the finite width of the Landau bands is due to disorder only. The superlattice modulation potential yields a fractal splitting of the Landau levels into Hofstadter minibands. For rational flux through a unit cell, the minibands have a finite width and intrinsic dispersion relations. We consider a regime, now accessible experimentally, in which disorder does not wash out the fractal internal gap structure of the Landau bands completely. We found the following distinctions from the conventional IQHE produced by the superlattice: (i) the peaks in diagonal conductivity are split due to the Hofstadter miniband structure of Landau bands; (ii) the number of split peaks in the bunch, their positions and heights depend irregularly on the magnetic field and the Fermi energy; (iii) the gaps between the split Landau bands (and related quantum Hall plateaus) become narrower with the superlattice modulation than without it.
International Nuclear Information System (INIS)
Gurtovoi, V. L.; Dubonos, S. V.; Karpii, S. V.; Nikulov, A. V.; Tulin, V. A.
2007-01-01
Magnetic field dependences of critical current, resistance, and rectified voltage of asymmetric (half circles of different widths) and symmetrical (half circles of equal widths) aluminum rings close to the super-conducting transition were measured. All these dependences are periodic magnetic field functions with periods corresponding to the flux quantum in the ring. The periodic dependences of critical current measured in opposite directions were found to be close to each other for symmetrical rings and shifted with respect to each other by half the flux quantum in asymmetric rings with ratios between half circle widths of from 1.25 to 2. This shift of the dependences by a quarter of the flux quantum as the ring becomes asymmetric makes critical current anisotropic, which explains the effect of alternating current rectification observed for asymmetric rings. Shifts of the extrema of the periodic dependences of critical current by a quarter of the flux quantum directly contradict the results obtained by measuring asymmetric ring resistance oscillations, whose extrema are, as for symmetrical rings, observed at magnetic fluxes equal to an integer and a half of flux quanta
Directory of Open Access Journals (Sweden)
Suhufa Alfarisa
2016-03-01
Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free density functional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.
Man'ko, V I
1993-01-01
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.
One dimension harmonic oscillator
International Nuclear Information System (INIS)
Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.
1977-01-01
The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr
International Nuclear Information System (INIS)
Mota, R D; Xicotencatl, M A; Granados, V D
2004-01-01
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse
Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.
2004-02-01
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)
2004-02-20
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
International Nuclear Information System (INIS)
Giri, Pulak Ranjan
2007-01-01
We perform a one-parameter family of self-adjoint extensions characterized by the parameter ω 0 . This allows us to get generic boundary conditions for the quantum oscillator on N-dimensional complex projective space (CP N ) and on its non-compact version, i.e., Lobachewski space (L N ) in the presence of a constant magnetic field. As a result, we get a family of energy spectra for the oscillator. In our formulation the already known result of this oscillator also belongs to the family. We have also obtained an energy spectrum which preserves all the symmetries (full-hidden symmetry and rotational symmetry) of the oscillator. The method of self-adjoint extensions has also been discussed for a conic oscillator in the presence of the constant magnetic field
Quantum classical correspondence in a 2-dimensional deformed harmonic oscillator system
International Nuclear Information System (INIS)
Liu Fang; Li Junqing; Xing Yongzhong
2002-01-01
The time evolution of expectation values of the basic dynamic variables in a quantum system under different effective Planck constant were compared with the exact values of the basic dynamic variables in classical system. It is found, for the regular motion, the difference comes from the quantum effect; for the chaotic motion, it comes from the dynamical effect and the destruction of the dynamical system. With these results, a correspondence between the quantum heterogeneity of the phase space and the Lyapunov exponent is made satisfactorily
Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects
International Nuclear Information System (INIS)
Ghosh, Subir; Majhi, Bibhas Ranjan
2008-01-01
We study complexified harmonic oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) who initiated the study of these Crypto-gauge invariant models that can be related to PT-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints (in contrast to Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) where one deals with a single constraint) with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator
Special function solutions of a spectral problem for a nonlinear quantum oscillator
International Nuclear Information System (INIS)
Schulze-Halberg, A; Morris, J R
2012-01-01
We construct exact solutions of a spectral problem involving the Schrödinger equation for a nonlinear, one-parameter oscillator potential. In contrast to a previous analysis of the problem (Carinena et al 2007 Ann. Phys. 322 434–59), where solutions were given through a Rodrigues-type formula, our approach leads to closed-form representations of the solutions in terms of special functions, not containing any derivative operators. We show normalizability and orthogonality of our solutions, as well as correct reduction of the problem to the harmonic oscillator model, if the parameter in the potential gets close to zero. (paper)
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
International Nuclear Information System (INIS)
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-01-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number. (paper)
De Raedt, Hans; Barbara, Bernard; Miyashita, Seiji; Michielsen, Kristel; Bertaina, Sylvain; Gambarelli, Serge
2012-01-01
Electron paramagnetic resonance experiments show that the decay of Rabi oscillations of ensembles of spin qubits depends noticeably on the microwave power, and more precisely on the Rabi frequency, an effect recently called "driven decoherence." By direct numerical solution of the time-dependent
International Nuclear Information System (INIS)
Svirskii, M.S.
1985-01-01
Oscillations with a period equal to the normal or superconducting flux quantum occur in the current density and the orbital parts of the energy and the magnetic moment in cyclic systems. Transitions between these regimes can be induced by changing the number of electrons or by switching between states with different energies
Biswas, Subhadip; Chattopadhyay, Rohitashwa; Bhattacharjee, Jayanta K.
2018-05-01
We consider the dynamics of a particle in a parametric oscillator with a view to exploring any quantum feature of the initial wave packet that shows divergent (in time) behaviour for parameter values where the classical motion dynamics of the mean position is bounded. We use Ehrenfest's theorem to explore the dynamics of nth order moment which reduces exactly to a linear non autonomous differential equation of order n + 1. It is found that while the width and skewness of the packet is unbounded exactly in the zones where the classical motion is unbounded, the kurtosis of an initially non-gaussian wave packet can become infinitely large in certain additional zones. This implies that the shape of the wave packet can change drastically with time in these zones.
Strain-mediated coupling in a quantum dot-mechanical oscillator hybrid system.
Yeo, I; de Assis, P-L; Gloppe, A; Dupont-Ferrier, E; Verlot, P; Malik, N S; Dupuy, E; Claudon, J; Gérard, J-M; Auffèves, A; Nogues, G; Seidelin, S; Poizat, J-Ph; Arcizet, O; Richard, M
2014-02-01
Recent progress in nanotechnology has allowed the fabrication of new hybrid systems in which a single two-level system is coupled to a mechanical nanoresonator. In such systems the quantum nature of a macroscopic degree of freedom can be revealed and manipulated. This opens up appealing perspectives for quantum information technologies, and for the exploration of the quantum-classical boundary. Here we present the experimental realization of a monolithic solid-state hybrid system governed by material strain: a quantum dot is embedded within a nanowire that features discrete mechanical resonances corresponding to flexural vibration modes. Mechanical vibrations result in a time-varying strain field that modulates the quantum dot transition energy. This approach simultaneously offers a large light-extraction efficiency and a large exciton-phonon coupling strength g0. By means of optical and mechanical spectroscopy, we find that g0/2 π is nearly as large as the mechanical frequency, a criterion that defines the ultrastrong coupling regime.
Energy Technology Data Exchange (ETDEWEB)
Knolle, Johannes; Cooper, Nigel [T.C.M. Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE (United Kingdom)
2016-07-01
The de Haas-van Alphen effect (dHvAE), describing oscillations of the magnetization as a function of magnetic field, is commonly assumed to be a definite sign for the presence of a Fermi surface (FS). Indeed, the effect forms the basis of a well-established experimental procedure for accurately measuring FS topology and geometry of metallic systems, with parameters commonly extracted by fitting to the Lifshitz-Kosevich (LK) theory based on Fermi liquid theory. Here we show that, in contrast to this canonical situation, there can be quantum oscillations even for band insulators of certain types. We provide simple analytic formulas describing the temperature dependence of the quantum oscillations in this setting, showing strong deviations from LK theory. We draw connections to recent experiments on the tentative topological Kondo insulator SmB{sub 6}.
Brownian dynamics with hydrodynamic interactions
International Nuclear Information System (INIS)
Ermak, D.L.; McCammon, J.A.
1978-01-01
A method for simulating the Brownian dynamics of N particles with the inclusion of hydrodynamic interactions is described. The particles may also be subject to the usual interparticle or external forces (e.g., electrostatic) which have been included in previous methods for simulating Brownian dynamics of particles in the absence of hydrodynamic interactions. The present method is derived from the Langevin equations for the N particle assembly, and the results are shown to be consistent with the corresponding Fokker--Planck results. Sample calculations on small systems illustrate the importance of including hydrodynamic interactions in Brownian dynamics simulations. The method should be useful for simulation studies of diffusion limited reactions, polymer dynamics, protein folding, particle coagulation, and other phenomena in solution
Grifoni, Milena
1997-01-01
In this thesis, ratchet systems operating in the quantum regime are investigated. Ratchet systems, also known as Brownian motors, are periodic systems presenting an intrinsic asymmetry which can be exploited to extract work out of unbiased forces. As a model for ratchet systems, we consider the motion of a particle in a one-dimensional periodic and asymmetric potential, interacting with a thermal environment, and subject to an unbiased driving force. In quantum ratchets, intrinsic quantum flu...
Brownian movement and molecular reality
Perrin, Jean
2005-01-01
How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this ""Brownian motion"" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownia
Prediction of femtosecond oscillations in the transient current of a quantum dot in the Kondo regime
Goker, A.
2010-10-11
We invoke the time-dependent noncrossing approximation in order to study the effects of the density of states of gold contacts on the instantaneous conductance of a single electron transistor which is abruptly moved into the Kondo regime by means of a gate voltage. For an asymmetrically coupled system, we observe that the instantaneous conductance in the Kondo time scale exhibits beating with distinct frequencies, which are proportional to the separation between the Fermi level and the sharp features in the density of states of gold. Increasing the ambient temperature or bias quenches the amplitude of the oscillations. We attribute the oscillations to interference between the emerging Kondo resonance and van-Hove singularities in the density of state. In addition, we propose an experimental realization of this model.
Topological nature of the node-arc semimetal PtSn4 probed by de Haas-van Alphen quantum oscillations
Wang, Y. J.; Liang, D. D.; Ge, M.; Yang, J.; Gong, J. X.; Luo, L.; Pi, L.; Zhu, W. K.; Zhang, C. J.; Zhang, Y. H.
2018-04-01
Dirac node arc semimetal state is a new topological quantum state which is proposed to exist in PtSn4 (Wu et al 2016 Dirac node arcs in PtSn4 Nat. Phys. 12 667–71). We present a systematic de Haas-van Alphen quantum oscillation study on this compound. Two intriguing oscillation branches, i.e. F 1 and F 2, are detected in the fast Fourier transformation spectra, both of which are characterized to possess tiny effective mass and ultrahigh quantum mobility. And the F 2 branch exhibits an angle-dependent nontrivial Berry phase. The features are consistent with the existence of the node arc semimetal state and shed new light on its complicated Fermi surfaces and topological nature.
Quantum oscillations of thermomagnetic coefficients of layered conductors in a strong magnetic field
International Nuclear Information System (INIS)
Kirichenko, O.V.; Kozlov, I.V.; Peschansky, V.G.; Krstovska, D.
2008-01-01
The linear response of the electronic system of a conductor to a perturbation in the form of an electric field and a temperature gradient in a quantizing magnetic field B is investigated theoretically. The thermoelectric effect in a layered conductor is analyzed and it is shown that the quasi-two-dimensional character of the dispersion law of the charge carriers results in gigantic oscillations of the thermo-emf
Synchronization and collective motion of globally coupled Brownian particles
International Nuclear Information System (INIS)
Sevilla, Francisco J; Heiblum-Robles, Alexandro; Dossetti, Victor
2014-01-01
In this work, we study a system of passive Brownian (non-self-propelled) particles in two dimensions, interacting only through a social-like force (velocity alignment in this case) that resembles Kuramoto's coupling among phase oscillators. We show that the kinematical stationary states of the system go from a phase in thermal equilibrium with no net flux of particles, to far-from-equilibrium phases exhibiting collective motion by increasing the coupling among particles. The mechanism that leads to the instability of the equilibrium phase relies on the competition between two time scales, namely, the mean collision time of the Brownian particles in a thermal bath and the time it takes for a particle to orient its direction of motion along the direction of motion of the group. Our results show a clear connection between collective motion and the Kuramoto model for synchronization, in our case, for the direction of motion of the particles. (paper)
Entropic Approach to Brownian Movement.
Neumann, Richard M.
1980-01-01
A diffusional driving force, called the radial force, which is responsible for the increase with time of the scalar separation between a fixed point and a particle undergoing three-dimensional Brownian motion, is derived using Boltzmann's equation. (Author/HM)
Coherent oscillation in a linear quantum system coupled to a thermal bath
International Nuclear Information System (INIS)
Bell, N.F.; Volkas, R.R.; Sawyer, R.F.
2000-01-01
We consider the time development of the density matrix for a system coupled to a thermal bath, in models that go beyond the standard two-level systems through addition of an energy excitation degree of freedom and through the possibility of the replacement of the spin algebra by a more complex algebra. We find conditions under which increasing the coupling to the bath above a certain level decreases the rate of entropy production, and in which the limiting behavior is a dissipationless sinusoidal oscillation that could be interpreted as the synchronization of many modes of the uncoupled system
Quantum dynamics of an electric charge in an oscillating pulsed magnetic field
International Nuclear Information System (INIS)
Oliveira, I.S.; Guimaraes, A.P.; Silva, X.A. da
1996-11-01
The motion of a charged particle under the action of a time-dependent oscillating magnetic field has been investigated. For one and two magnetic pulses were obtained analytical expressions for the free current decay and current echo in agreement with a recently proposed classical description of electrical current in fields E and B. When the resonance condition is achieved, the axis of quantization is turned over by 90 degrees. The results suggest a magnetic pulsed resonant method to separate charged particles in a beam. (author). 12 refs
Adventures of the coupled Yang-Mills oscillators: II. YM-Higgs quantum mechanics
International Nuclear Information System (INIS)
Matinyan, Sergei G; Mueller, Berndt
2006-01-01
We continue our study of the quantum mechanical motion in the x 2 y 2 potentials for n = 2, 3, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. In the present paper, we develop a new approach to the calculation of the partition function Z(t) beyond the Thomas-Fermi (TF) approximation by adding a harmonic (Higgs) potential and taking the limit v → 0, where v is the vacuum expectation value of the Higgs field. Using the Wigner-Kirkwood method to calculate higher-order corrections in ℎ, we show that the limit v → 0 leads to power-like singularities of the type v -n , which reflect the possibility of escape of the particle along the channels in the classical limit. We show how these singularities can be eliminated by taking into account the quantum fluctuations dictated by the form of the potential
Oscillations of quantum transport through double-AB rings with magnetic impurity
International Nuclear Information System (INIS)
Gao Yingfang; Liang, J-Q
2006-01-01
We have studied the effect of impurity scattering on the quantum transport through double AB rings in the presence of spin-flipper in the middle lead in terms of one-dimensional quantum waveguide theory. The electron interacts with the impurity through the exchange interaction leading to spin-flip scattering. Transmissions in the spin-flipped and non-spin-flipped channels are calculated explicitly. It is found that the overall transmission and the conductance are distorted due to the impurity scattering. The extent of distortion not only depends on the strength of the impurity potential but also on the impurity position. Moreover, the transmission probability and the conductance are modulated by the magnetic flux, the size of the ring and the impurity potential strength as well
EASTHAM, PAUL
2003-01-01
PUBLISHED We connect three phenomena in which a coherent electromagnetic field could be generated: polariton condensation, phase-locking in arrays of underdamped Josephson junctions, and lasing. All these phenomena have been described using Dicke-type models of spins coupled to a single photon mode. These descriptions may be distinguished by whether the spins are quantum or classical, and whether they are strongly or weakly damped.
A numerical study of the quantum oscillations in multiple dangling rings
International Nuclear Information System (INIS)
Gu, B.Y.; Basu, C.
1994-12-01
We present the quantum mechanical calculations on magnetoconductance of the quantum waveguide topology containing multiply connected dangling mesoscopic rings with the transfer matrix approach. The profiles of the conductance as functions of the Fermi wave number of electrons and of the magnetic flux depend on the number of rings as also on the geometric configuration of the system. The conductance spectrum of this system for disordered lengths in the ring circumferences, dangling links, ballistic leads connecting consecutive dangling rings and disordered magnetic flux is examined in details. We find that there exist two kinds of mini-bands, one originating from the eigenstates of the rings, i.e. the intrinsic mini-bands, and the extra mini-bands. Some of these extra minibands are associated with the dangling links connecting the rings to the main quantum wire, while others are from the standing wave modes associated with the ballistic leads connecting adjacent dangling rings. These different kinds of mini-bands have completely different properties and responds differently to the geometric parameter fluctuations. Unlike the system of potential scatterers, this system of geometric scatterers shows complete band formations at all energies even for finite number of scatterers present. There is a preferential decay of the energy states, depending upon the type of disorder introduced. By controlling the geometric parameters, the conductance band structure of such a model can be artificially tailored and thus may guide the design of better mesoscopic switching devices. (author). 19 refs, 7 figs
Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics
Directory of Open Access Journals (Sweden)
Giovanni Modanese
Full Text Available We show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field zone and wave zone is blurred. We employ an extension of Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with currents jν conserved globally but not locally; we have derived in another work the field equation ∂μFμν=jν+iν, where iν is a non-local function of jν, called “secondary current”. Y. Wei has recently proved that the probability current in fractional quantum mechanics is in general not locally conserved. We compute this current for a Gaussian wave packet with fractional parameter a=3/2 and find that in a suitable limit it can be approximated by our simplified dipolar source. Currents which are not locally conserved may be present also in other quantum systems whose wave functions satisfy non-local equations. The combined electromagnetic effects of such sources and their secondary currents are very interesting both theoretically and for potential applications. Keywords: Generalized Maxwell theory, Fractional Schrödinger equation, Local current conservation
Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-Line Semimetals
Li, Cequn; Wang, C. M.; Wan, Bo; Wan, Xiangang; Lu, Hai-Zhou; Xie, X. C.
2018-04-01
Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial π Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W =Zr /Hf , H =Si /Ge , M =S /Se /Te ). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu3 PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help explore transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.
International Nuclear Information System (INIS)
Mahajan, Sonam; Aggarwal, Neha; ManMohan; Bhattacherjee, Aranya B
2013-01-01
We present a detailed study to show the possibility of approaching the quantum ground state of a hybrid optomechanical quantum device formed by a Bose–Einstein condensate (BEC) confined inside a high-finesse optical cavity with an oscillatory end mirror. Cooling is achieved using two experimentally realizable schemes: back-action cooling and cold damping quantum feedback cooling. In both the schemes, we found that increasing the two-body atom–atom interaction brings the mechanical oscillator to its quantum ground state. It has been observed that back-action cooling is more effective in the good cavity limit, while the cold damping cooling scheme is more relevant in the bad cavity limit. It is also shown that in the cold damping scheme, the device is more efficient in the presence of a BEC than in the absence of a BEC. (paper)
Barzola-Quiquia, J; Klingner, N; Krüger, J; Molle, A; Esquinazi, P; Leonhardt, A; Martínez, M T
2012-01-13
We report on the electrical transport properties of single multiwall carbon nanotubes with and without an iron filling as a function of temperature and magnetic field. For the iron filled nanotubes the magnetoresistance shows a magnetic behavior induced by iron, which can be explained by taking into account a contribution of s-d hybridization. In particular, ferromagnetic-like hysteresis loops were observed up to 50 K for the iron filled multiwall carbon nanotubes. The magnetoresistance shows quantum interference phenomena such as universal conductance fluctuations and weak localization effects.
Quantum oscillations and ferromagnetic hysteresis observed in iron filled multiwall carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Barzola-Quiquia, Jose; Klingner, Niko; Molle, Axel [Division of Superconductivity and Magnetism, University of Leipzig, D-04103 Leipzig (Germany); Leonhardt, Albrecht [Leibniz Institute for Solid State and Materials Research (IFW) Dresden, Helmholtzstrasse 20, 01069 Dresden (Germany)
2011-07-01
Carbon-based materials as multiwall carbon nanotubes (MWCNT) are attractive for spintronics because spin is only weakly coupled to the lattice, leading to large spin-flip scattering length and long spin relaxation times. In this contribution we have investigated the electrical transport properties of iron filled MWCNT (outer diameter 150 nm, inner diameter 25 nm and length 2000 nm) as a function of temperature and magnetic field. We observed quantum interference effects, i.e. universal conductance fluctuations, and weak localization effects. The in-plane magnetoresistance shows typical butterfly structure revealing the ferromagnetic properties of the Fe-filled MWCNT. The ferromagnetic hysteresis was observed up to 40K.
International Nuclear Information System (INIS)
Chakravarty, Sudip
2011-01-01
High temperature superconductivity in cuprate superconductors remains an unsolved problem in theoretical physics. The same statement can also be made about a number of other superconductors that have been dubbed novel. What makes these superconductors so elusive is an interesting question in itself. This paper focuses on the recent magnetic oscillation experiments and how they fit into the broader picture. Many aspects of these experiments can be explained by Fermi liquid theory; the key issue is the extent to which this is true. If true, the entire paradigm developed over the past three decades must be reexamined. A critical analysis of this issue has necessitated a broader analysis of questions about distinct ground states of matter, which may be useful in understanding other novel superconductors.
High electron mobility and quantum oscillations in non-encapsulated ultrathin semiconducting Bi2O2Se
Wu, Jinxiong; Yuan, Hongtao; Meng, Mengmeng; Chen, Cheng; Sun, Yan; Chen, Zhuoyu; Dang, Wenhui; Tan, Congwei; Liu, Yujing; Yin, Jianbo; Zhou, Yubing; Huang, Shaoyun; Xu, H. Q.; Cui, Yi; Hwang, Harold Y.; Liu, Zhongfan; Chen, Yulin; Yan, Binghai; Peng, Hailin
2017-07-01
High-mobility semiconducting ultrathin films form the basis of modern electronics, and may lead to the scalable fabrication of highly performing devices. Because the ultrathin limit cannot be reached for traditional semiconductors, identifying new two-dimensional materials with both high carrier mobility and a large electronic bandgap is a pivotal goal of fundamental research. However, air-stable ultrathin semiconducting materials with superior performances remain elusive at present. Here, we report ultrathin films of non-encapsulated layered Bi2O2Se, grown by chemical vapour deposition, which demonstrate excellent air stability and high-mobility semiconducting behaviour. We observe bandgap values of ˜0.8 eV, which are strongly dependent on the film thickness due to quantum-confinement effects. An ultrahigh Hall mobility value of >20,000 cm2 V-1 s-1 is measured in as-grown Bi2O2Se nanoflakes at low temperatures. This value is comparable to what is observed in graphene grown by chemical vapour deposition and at the LaAlO3-SrTiO3 interface, making the detection of Shubnikov-de Haas quantum oscillations possible. Top-gated field-effect transistors based on Bi2O2Se crystals down to the bilayer limit exhibit high Hall mobility values (up to 450 cm2 V-1 s-1), large current on/off ratios (>106) and near-ideal subthreshold swing values (˜65 mV dec-1) at room temperature. Our results make Bi2O2Se a promising candidate for future high-speed and low-power electronic applications.
Polynomial deformations of oscillator algebras in quantum theories with internal symmetries
International Nuclear Information System (INIS)
Karassiov, V.P.
1992-01-01
This paper reports that for last years some new Lie-algebraic structures (quantum groups or algebras, W-algebras, Casimir algebras) have been introduced in different areas of modern physics. All these objects are non-linear generalizations (deformations) of usual (linear) Lie algebras which are generated by a set B = {T a } of their generators T a satisfying a commutation relations (CR) of the form [T a , T b ] = f ab ({T c }) where f ab (...) are some functions of the generators T c given by power series. From the mathematical viewpoint such objects called as nonlinear or deformed Lie algebras G d may be treated as universal algebras or algebraic systems G d = left-angle B; +, · , [,] right-angle generated by a basic set B and the usual operations of the addition (+) and the multiplication (·) together with the Lie product ([T a , T b ] = T a T b - T b T a )
Slow kinetics of Brownian maxima.
Ben-Naim, E; Krapivsky, P L
2014-07-18
We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Czech Academy of Sciences Publication Activity Database
Mikhailova, M. P.; Veinger, A.I.; Kochman, I.V.; Semenikhin, P.V.; Kalinina, K.V.; Parfeniev, R.V.; Berezovets, V.A.; Safonchik, M.O.; Hospodková, Alice; Pangrác, Jiří; Zíková, Markéta; Hulicius, Eduard
2016-01-01
Roč. 10, č. 4 (2016), 1-8, č. článku 046013. ISSN 1934-2608 R&D Projects: GA ČR GA13-15286S; GA MŠk LO1603 Institutional support: RVO:68378271 Keywords : Shubnikov-de Haas oscillations * microwave absorption * electron-paramagnetic resonance * composite quantum wells * InAs/GaSb/AlSb * MOVPE Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.325, year: 2016
Random motion and Brownian rotation
International Nuclear Information System (INIS)
Wyllie, G.
1980-01-01
The course is centred on the Brownian motion - the random movement of molecules arising from thermal fluctuations of the surrounding medium - and starts with the classical theory of A. Einstein, M.v. Smoluchowski and P. Langevin. The first part of this article is quite elementary, and several of the questions raised in it have been instructively treated in a much more sophisticated way in recent reviews by Pomeau and Resibois and by Fox. This simple material may nevertheless be helpful to some readers whose main interest lies in approaching the work on Brownian rotation reviewed in the latter part of the present article. The simplest, and most brutally idealised, problem in our field of interest is that of the random walk in one dimension of space. Its solution leads on, through the diffusivity-mobility relation of Einstein, to Langevin's treatment of the Brownian motion. The application of these ideas to the movement of a molecule in a medium of similar molecules is clearly unrealistic, and much energy has been devoted to finding a suitable generalisation. We shall discuss in particular ideas due to Green, Zwanzig and Mori. (orig./WL)
Castellano, Fabrizio; Li, Lianhe; Linfield, Edmund H; Davies, A Giles; Vitiello, Miriam S
2016-03-15
Mode-locked comb sources operating at optical frequencies underpin applications ranging from spectroscopy and ultrafast physics, through to absolute frequency measurements and atomic clocks. Extending their operation into the terahertz frequency range would greatly benefit from the availability of compact semiconductor-based sources. However, the development of any compact mode-locked THz laser, which itself is inherently a frequency comb, has yet to be achieved without the use of an external stimulus. High-power, electrically pumped quantum cascade lasers (QCLs) have recently emerged as a promising solution, owing to their octave spanning bandwidths, the ability to achieve group-velocity dispersion compensation and the possibility of obtaining active mode-locking. Here, we propose an unprecedented compact architecture to induce both frequency and amplitude self-modulation in a THz QCL. By engineering a microwave avalanche oscillator into the laser cavity, which provides a 10 GHz self-modulation of the bias current and output power, we demonstrate multimode laser emission centered around 3 THz, with distinct multiple sidebands. The resulting microwave amplitude and frequency self-modulation of THz QCLs opens up intriguing perspectives, for engineering integrated self-mode-locked THz lasers, with impact in fields such as nano- and ultrafast photonics and optical metrology.
Operator Fractional Brownian Motion and Martingale Differences
Directory of Open Access Journals (Sweden)
Hongshuai Dai
2014-01-01
Full Text Available It is well known that martingale difference sequences are very useful in applications and theory. On the other hand, the operator fractional Brownian motion as an extension of the well-known fractional Brownian motion also plays an important role in both applications and theory. In this paper, we study the relation between them. We construct an approximation sequence of operator fractional Brownian motion based on a martingale difference sequence.
Theory of Brownian motion with the Alder-Wainwright effect
International Nuclear Information System (INIS)
Okabe, Y.
1986-01-01
The Stokes-Boussinesq-Langevin equation, which describes the time evolution of Brownian motion with the Alder-Wainwright effect, can be treated in the framework of the theory of KMO-Langevin equations which describe the time evolution of a real, stationary Gaussian process with T-positivity (reflection positivity) originating in axiomatic quantum field theory. After proving the fluctuation-dissipation theorems for KMO-Langevin equations, the authors obtain an explicit formula for the deviation from the classical Einstein relation that occurs in the Stokes-Boussinesq-Langevin equation with a white noise as its random force. The authors interested in whether or not it can be measured experimentally
Rotational and translational Brownian motion
International Nuclear Information System (INIS)
Coffey, W.T.; Salford Univ.
1980-01-01
In this review it is proposed to summarise the work on the theory of the translational and rotational Brownian movement which has been carried on over roughly the past 30 years. The review is intended to take the form of a tutorial paper rather than a list of the results obtained by the various investigators over the period in question. In this vein then it seems appropriate to firstly give a brief account of those parts of the theory of probability which are relevant to the problems under discussion. (orig.)
Brownian Optimal Stopping and Random Walks
International Nuclear Information System (INIS)
Lamberton, D.
2002-01-01
One way to compute the value function of an optimal stopping problem along Brownian paths consists of approximating Brownian motion by a random walk. We derive error estimates for this type of approximation under various assumptions on the distribution of the approximating random walk
International Nuclear Information System (INIS)
Anon.
1990-01-01
The book is on quantum mechanics. The emphasis is on the basic concepts and the methodology. The chapters include: Breakdown of classical concepts; Quantum mechanical concepts; Basic postulates of quantum mechanics; solution of problems in quantum mechanics; Simple harmonic oscillator; and Angular Momentum
Brownian motion of tethered nanowires.
Ota, Sadao; Li, Tongcang; Li, Yimin; Ye, Ziliang; Labno, Anna; Yin, Xiaobo; Alam, Mohammad-Reza; Zhang, Xiang
2014-05-01
Brownian motion of slender particles near a boundary is ubiquitous in biological systems and in nanomaterial assembly, but the complex hydrodynamic interaction in those systems is still poorly understood. Here, we report experimental and computational studies of the Brownian motion of silicon nanowires tethered on a substrate. An optical interference method enabled direct observation of microscopic rotations of the slender bodies in three dimensions with high angular and temporal resolutions. This quantitative observation revealed anisotropic and angle-dependent hydrodynamic wall effects: rotational diffusivity in inclined and azimuth directions follows different power laws as a function of the length, ∼ L(-2.5) and ∼ L(-3), respectively, and is more hindered for smaller inclined angles. In parallel, we developed an implicit simulation technique that takes the complex wire-wall hydrodynamic interactions into account efficiently, the result of which agreed well with the experimentally observed angle-dependent diffusion. The demonstrated techniques provide a platform for studying the microrheology of soft condensed matters, such as colloidal and biological systems near interfaces, and exploring the optimal self-assembly conditions of nanostructures.
Dyksik, Mateusz; Motyka, Marcin; Kurka, Marcin; Ryczko, Krzysztof; Misiewicz, Jan; Schade, Anne; Kamp, Martin; Höfling, Sven; Sęk, Grzegorz
2017-11-01
Two designs of active region for an interband cascade laser, based on double or triple GaInSb/InAs type II quantum wells (QWs), were compared with respect to passive mode-locked operation in the mid-infrared range around 4 µm. The layer structure and electron and hole wavefunctions under external electric field were engineered to allow controlling the optical transition oscillator strength and the resulting lifetimes. As a result, the investigated structures can mimic absorber-like and gain-like sections of a mode-locked device when properly polarized with opposite bias. A significantly larger oscillator strength tuning range for triple QWs was experimentally verified by Fourier-transform photoreflectance.
Brownian ratchets from statistical physics to bio and nano-motors
Cubero, David
2016-01-01
Illustrating the development of Brownian ratchets, from their foundations, to their role in the description of life at the molecular scale and in the design of artificial nano-machinery, this text will appeal to both advanced graduates and researchers entering the field. Providing a self-contained introduction to Brownian ratchets, devices which rectify microscopic fluctuations, Part I avoids technicalities and sets out the broad range of physical systems where the concept of ratchets is relevant. Part II supplies a single source for a complete and modern theoretical analysis of ratchets in regimes such as classical vs quantum and stochastic vs deterministic, and in Part III readers are guided through experimental developments in different physical systems, each highlighting a specific unique feature of ratchets. The thorough and systematic approach to the topic ensures that this book provides a complete guide to Brownian ratchets for newcomers and established researchers in physics, biology and biochemistry.
Achieving swift equilibration of a Brownian particle using flow-fields
Patra, Ayoti; Jarzynski, Christopher
Can a system be driven to a targeted equilibrium state on a timescale that is much shorter than its natural equilibration time? In a recent experiment, the swift equilibration of an overdamped Brownian particle was achieved by use of an appropriately designed, time-dependent optical trap potential. Motivated by these results, we develop a general theoretical approach for guiding an ensemble of Brownian particles to track the instantaneous equilibrium distribution of a desired potential U (q , t) . In our approach, we use flow-fields associated with the parametric evolution of the targeted equilibrium state to construct an auxiliary potential U (q , t) , such that dynamics under the composite potential U (t) + U (t) achieves the desired evolution. Our results establish a close connection between the swift equilibration of Brownian particles, quantum shortcuts to adiabaticity, and the dissipationless driving of a classical, Hamiltonian system.
A multiscale guide to Brownian motion
International Nuclear Information System (INIS)
Grebenkov, Denis S; Belyaev, Dmitry; Jones, Peter W
2016-01-01
We revise the Lévy construction of Brownian motion as a simple though rigorous approach to operate with various Gaussian processes. A Brownian path is explicitly constructed as a linear combination of wavelet-based ‘geometrical features’ at multiple length scales with random weights. Such a wavelet representation gives a closed formula mapping of the unit interval onto the functional space of Brownian paths. This formula elucidates many classical results about Brownian motion (e.g., non-differentiability of its path), providing an intuitive feeling for non-mathematicians. The illustrative character of the wavelet representation, along with the simple structure of the underlying probability space, is different from the usual presentation of most classical textbooks. Similar concepts are discussed for the Brownian bridge, fractional Brownian motion, the Ornstein-Uhlenbeck process, Gaussian free fields, and fractional Gaussian fields. Wavelet representations and dyadic decompositions form the basis of many highly efficient numerical methods to simulate Gaussian processes and fields, including Brownian motion and other diffusive processes in confining domains. (topical review)
Corzo, H. H.; Velasco, A. M.; Lavín, C.; Ortiz, J. V.
2018-02-01
Vertical excitation energies belonging to several Rydberg series of MgH have been inferred from 3+ electron-propagator calculations of the electron affinities of MgH+ and are in close agreement with experiment. Many electronically excited states with n > 3 are reported for the first time and new insight is given on the assignment of several Rydberg series. Valence and Rydberg excited states of MgH are distinguished respectively by high and low pole strengths corresponding to Dyson orbitals of electron attachment to the cation. By applying the Molecular Quantum Defect Orbital method, oscillator strengths for electronic transitions involving Rydberg states also have been determined.
International Nuclear Information System (INIS)
Santos Coelho, Leandro dos; Mariani, Viviana Cocco
2008-01-01
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature
Energy Technology Data Exchange (ETDEWEB)
dos Santos Coelho, Leandro [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil); Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Santos Coelho, Leandro dos [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: leandro.coelho@pucpr.br; Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: viviana.mariani@pucpr.br
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.
International Nuclear Information System (INIS)
Ayvaz, Muzaffer; Demiralp, Metin
2011-01-01
In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.
Stock price prediction using geometric Brownian motion
Farida Agustini, W.; Restu Affianti, Ika; Putri, Endah RM
2018-03-01
Geometric Brownian motion is a mathematical model for predicting the future price of stock. The phase that done before stock price prediction is determine stock expected price formulation and determine the confidence level of 95%. On stock price prediction using geometric Brownian Motion model, the algorithm starts from calculating the value of return, followed by estimating value of volatility and drift, obtain the stock price forecast, calculating the forecast MAPE, calculating the stock expected price and calculating the confidence level of 95%. Based on the research, the output analysis shows that geometric Brownian motion model is the prediction technique with high rate of accuracy. It is proven with forecast MAPE value ≤ 20%.
Brownian motion using video capture
International Nuclear Information System (INIS)
Salmon, Reese; Robbins, Candace; Forinash, Kyle
2002-01-01
Although other researchers had previously observed the random motion of pollen grains suspended in water through a microscope, Robert Brown's name is associated with this behaviour based on observations he made in 1828. It was not until Einstein's work in the early 1900s however, that the origin of this irregular motion was established to be the result of collisions with molecules which were so small as to be invisible in a light microscope (Einstein A 1965 Investigations on the Theory of the Brownian Movement ed R Furth (New York: Dover) (transl. Cowper A D) (5 papers)). Jean Perrin in 1908 (Perrin J 1923 Atoms (New York: Van Nostrand-Reinhold) (transl. Hammick D)) was able, through a series of painstaking experiments, to establish the validity of Einstein's equation. We describe here the details of a junior level undergraduate physics laboratory experiment where students used a microscope, a video camera and video capture software to verify Einstein's famous calculation of 1905. (author)
An adjustable Brownian heat engine
International Nuclear Information System (INIS)
Asfaw, Mesfin; Bekele, Mulugeta
2002-09-01
A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found a closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs either with maximum power or with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines. (author)
Quantal Brownian Motion from RPA dynamics: The master and Fokker-Planck equations
International Nuclear Information System (INIS)
Yannouleas, C.
1984-05-01
From the purely quantal RPA description of the damped harmonic oscillator and of the corresponding Brownian Motion within the full space (phonon subspace plus reservoir), a master equation (as well as a Fokker-Planck equation) for the reduced density matrix (for the reduced Wigner function, respectively) within the phonon subspace is extracted. The RPA master equation agrees with the master equation derived by the time-dependent perturbative approaches which utilize Tamm-Dancoff Hilbert spaces and invoke the rotating wave approximation. Since the RPA yields a full, as well as a contracted description, it can account for both the kinetic and the unperturbed oscillator momenta. The RPA description of the quantal Brownian Motion contrasts with the descriptions provided by the time perturbative approaches whether they invoke or not the rotating wave approximation. The RPA description also contrasts with the phenomenological phase space quantization. (orig.)
Isaacson, D.; Marchesin, D.; Paes-Leme, P. J.
1980-01-01
This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.
Brownian motion in a flowing fluid revisited
International Nuclear Information System (INIS)
Ramshaw, J.D.
1981-01-01
It is shown how the phenomenon of osmosis may be treated using the phenomenological theory of Brownian motion in a flowing fluid. The theory is also generalized to include viscous stresses in the particle and mixture momentum equations
Energy Technology Data Exchange (ETDEWEB)
Kawamata, Shuichi, E-mail: s-kawamata@riast.osakafu-u.ac.jp; Kawamura, Yuichi [Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531 (Japan); Research Organization for University-Community Collaborations, Osaka Prefecture University, Sakai 599-8570 (Japan); Hibino, Akira; Tanaka, Sho [Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531 (Japan)
2016-10-14
In order to develop optical devices for 2–3 μm wavelength regions, the InP-based InGaAs/GaAsSb type II multiple quantum well system has been investigated. By doping nitrogen into InGaAs layers, the system becomes effective in creating the optical devices with a longer wavelength. In this report, electrical transport properties are reported on the InGaAsN/GaAsSb type II system. The epitaxial layers with the single hetero or multiple quantum well structure on InP substrates are grown by the molecular beam epitaxy. The electrical resistance of samples with different nitrogen concentrations has been measured as a function of the magnetic field up to 9 Tesla at several temperatures between 2 and 6 K. The oscillation of the resistance due to the Shubnikov-de Haas (SdH) effect has been observed at each temperature. The effective mass is obtained from the temperature dependence of the amplitude of the SdH oscillations. The value of the effective mass increases from 0.048 for N = 0.0% to 0.062 for N = 1.2 and 1.5% as the nitrogen concentration increases. The mass enhancement occurs with corresponding to the reduction of the bandgap energy. These results are consistent with the band anticrossing model.
A multiscale approach to Brownian motors
International Nuclear Information System (INIS)
Pavliotis, G.A.
2005-01-01
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this Letter. Multiscale techniques are used to derive general formulae for the steady state particle current and the effective diffusion tensor. These formulae are then applied to calculate the effective diffusion coefficient for a Brownian particle in a periodic potential driven simultaneously by additive Gaussian white and colored noise. Our theoretical findings are supported by numerical simulations
Biased Brownian dynamics for rate constant calculation.
Zou, G; Skeel, R D; Subramaniam, S
2000-01-01
An enhanced sampling method-biased Brownian dynamics-is developed for the calculation of diffusion-limited biomolecular association reaction rates with high energy or entropy barriers. Biased Brownian dynamics introduces a biasing force in addition to the electrostatic force between the reactants, and it associates a probability weight with each trajectory. A simulation loses weight when movement is along the biasing force and gains weight when movement is against the biasing force. The sampl...
On some generalization of fractional Brownian motions
International Nuclear Information System (INIS)
Wang Xiaotian; Liang Xiangqian; Ren Fuyao; Zhang Shiying
2006-01-01
The multifractional Brownian motion (mBm) is a continuous Gaussian process that extends the classical fractional Brownian motion (fBm) defined by Barton and Vincent Poor [Barton RJ, Vincent Poor H. IEEE Trans Inform 1988;34(5):943] and Decreusefond and Ustuenel [Decreusefond L, Ustuenel AS. Potential Anal 1999;10:177]. In addition, an innovational representation of fBm is given
Deep inelastic collisions viewed as Brownian motion
International Nuclear Information System (INIS)
Gross, D.H.E.; Freie Univ. Berlin
1980-01-01
Non-equilibrium transport processes like Brownian motion, are studied since perhaps 100 years and one should ask why does one not use these theories to explain deep inelastic collision data. These theories have reached a high standard of sophistication, experience, and precision that I believe them to be very usefull for our problem. I will try to sketch a possible form of an advanced theory of Brownian motion that seems to be suitable for low energy heavy ion collisions. (orig./FKS)
Brownian quasi-particles in statistical physics
International Nuclear Information System (INIS)
Tellez-Arenas, A.; Fronteau, J.; Combis, P.
1979-01-01
The idea of a Brownian quasi-particle and the associated differentiable flow (with nonselfadjoint forces) are used here in the context of a stochastic description of the approach towards statistical equilibrium. We show that this quasi-particle flow acquires, at equilibrium, the principal properties of a conservative Hamiltonian flow. Thus the model of Brownian quasi-particles permits us to establish a link between the stochastic description and the Gibbs description of statistical equilibrium
International Nuclear Information System (INIS)
Sarkar, P.; Bhattacharyya, S.P.
1995-01-01
The effects of quartic anharmonicity on the quantum dynamics of a linear oscillator with time-dependent force constant (K) or harmonic frequency (ω) are studied both perturbatively and numerically by the time-dependent Fourier grid Hamiltonian method. In the absence of anharmonicity, the ground-state population decreases and the population of an accessible excited state (k = 2.4, 6 ... ) increases with time. However, when anharmonicity is introduced, both the ground- and excited-state populations show typical oscillations. For weak coupling, the population of an accessible excited state at a certain instant of time (short) turns out to be a parabolic function of the anharmonic coupling constant (λ), when all other parameters of the system are kept fixed. This parabolic nature of the excited-state population vs. the λ profile is independent of the specific form of the time dependence of the force constant, K t . However, it depends upon the rate at which K t relaxes. For small anharmonic coupling strength and short time scales, the numerical results corroborate expectations based on the first-order time-dependent perturbative analysis, using a suitably repartitioned Hamiltonian that makes H 0 time-independent. Some of the possible experimental implications of our observations are analyzed, especially in relation to intensity oscillations observed in some charge-transfer spectra in systems in which the dephasing rates are comparable with the time scale of the electron transfer. 21 refs., 7 figs., 1 tab
Directory of Open Access Journals (Sweden)
Partha Goswami
2010-01-01
Full Text Available We investigate a chiral d-density wave (CDDW mean field model Hamiltonian in the momentum space suitable for the hole-doped cuprates, such as YBCO, in the pseudogap phase to obtain the Fermi surface (FS topologies, including the anisotropy parameter(́ and the elastic scattering by disorder potential (|0|. For ́=0, with the chemical potential =−0.27 eV for 10% doping level and |0|≥|| (where ||=0.25 eV is the first neighbor hopping, at zero/non-zero magnetic field (, the FS on the first Brillouin zone is found to correspond to electron pockets around antinodal regions and barely visible patches around nodal regions. For ́≠0, we find Pomeranchuk distortion of FS. We next relate our findings regarding FS to the magneto-quantum oscillations in the electronic specific heat. Since the nodal quasiparticle energy values for =0 are found to be greater than for |0|≥||, the origin of the oscillations for nonzero corresponds to the Fermi pockets around antinodal regions. The oscillations are shown to take place in the weak disorder regime (|0|=0.25eV only.
The Schroedinger and Dirac free particle equations without quantum mechanics
International Nuclear Information System (INIS)
Ord, G.N.
1996-01-01
Einstein close-quote s theory of Brownian Movement has provided a well accepted microscopic model of diffusion for many years. Until recently the relationship between this model and Quantum Mechanics has been completely formal. Brownian motion provides a microscopic model for diffusion, but quantum mechanics and diffusion are related by a formal analytic continuation, so the relationship between Brownian motion and Quantum Mechanics has been correspondingly vague. Some recent work has changed this picture somewhat and here we show that a random walk model of Brownian motion produces the diffusion equation or the telegraph equations as a descriptions of particle densities, while at the same time the correlations in the space-time geometry of these same Brownian particles obey the Schroedinger and Dirac equations respectively. This is of interest because the equations of Quantum Mechanics appear here naturally in a classical context without the problems of interpretation they have in the usual context. copyright 1996 Academic Press, Inc
Lemkul, Justin A; MacKerell, Alexander D
2017-05-09
Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2016-05-15
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
Ge, Li; Zhao, Nan
2018-04-01
We study the coherence dynamics of a qubit coupled to a harmonic oscillator with both linear and quadratic interactions. As long as the linear coupling strength is much smaller than the oscillator frequency, the long time behavior of the coherence is dominated by the quadratic coupling strength g 2. The coherence decays and revives at a period , with the width of coherence peak decreasing as the temperature increases, hence providing a way to measure g 2 precisely without cooling. Unlike the case of linear coupling, here the coherence dynamics never reduces to the classical limit in which the oscillator is classical. Finally, the validity of linear coupling approximation is discussed and the coherence under Hahn-echo is evaluated.
Functionals of Brownian motion, localization and metric graphs
International Nuclear Information System (INIS)
Comtet, Alain; Desbois, Jean; Texier, Christophe
2005-01-01
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed: some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schroedinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of planar Brownian motion. (topical review)
Static structure of active Brownian hard disks
de Macedo Biniossek, N.; Löwen, H.; Voigtmann, Th; Smallenburg, F.
2018-02-01
We explore the changes in static structure of a two-dimensional system of active Brownian particles (ABP) with hard-disk interactions, using event-driven Brownian dynamics simulations. In particular, the effect of the self-propulsion velocity and the rotational diffusivity on the orientationally-averaged fluid structure factor is discussed. Typically activity increases structural ordering and generates a structure factor peak at zero wave vector which is a precursor of motility-induced phase separation. Our results provide reference data to test future statistical theories for the fluid structure of active Brownian systems. This manuscript was submitted for the special issue of the Journal of Physics: Condensed Matter associated with the Liquid Matter Conference 2017.
Eigenfunction expansion for fractional Brownian motions
International Nuclear Information System (INIS)
Maccone, C.
1981-01-01
The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)
International Nuclear Information System (INIS)
Chwiej, T; Szafran, B
2013-01-01
We study electron transfer across a two-terminal quantum ring using a time-dependent description of the scattering process. For the considered scattering event the quantum ring is initially charged with one or two electrons, with another electron incident to the ring from the input channel. We study the electron transfer probability (T) as a function of the external magnetic field. We determine the periodicity of T for a varied number of electrons confined within the ring. For that purpose we develop a method to describe the wave packet dynamics for a few electrons participating in the scattering process, taking into full account the electron–electron correlations. We find that electron transfer across the quantum ring initially charged by a single electron acquires a distinct periodicity of half of the magnetic flux quantum (Φ 0 /2), corresponding to the formation of a transient two-electron state inside the ring. In the case of a three-electron scattering problem with two electrons initially occupying the ring, a period of Φ 0 /3 for T is formed in the limit of thin channels. The effect of disorder present in the confinement potential of the ring is also discussed. (paper)
Chwiej, T; Szafran, B
2013-04-17
We study electron transfer across a two-terminal quantum ring using a time-dependent description of the scattering process. For the considered scattering event the quantum ring is initially charged with one or two electrons, with another electron incident to the ring from the input channel. We study the electron transfer probability (T) as a function of the external magnetic field. We determine the periodicity of T for a varied number of electrons confined within the ring. For that purpose we develop a method to describe the wave packet dynamics for a few electrons participating in the scattering process, taking into full account the electron-electron correlations. We find that electron transfer across the quantum ring initially charged by a single electron acquires a distinct periodicity of half of the magnetic flux quantum (Φ0/2), corresponding to the formation of a transient two-electron state inside the ring. In the case of a three-electron scattering problem with two electrons initially occupying the ring, a period of Φ0/3 for T is formed in the limit of thin channels. The effect of disorder present in the confinement potential of the ring is also discussed.
Kenkre, V. M.; Chase, M.
2017-08-01
The approach to equilibrium of a quantum mechanical system in interaction with a bath is studied from a practical as well as a conceptual point of view. Explicit memory functions are derived for given models of bath couplings. If the system is a harmonic oscillator representing a molecule in interaction with a reservoir, the generalized master equation derived becomes an extension into the coherent domain of the well-known Montroll-Shuler equation for vibrational relaxation and unimolecular dissociation. A generalization of the Bethe-Teller result regarding energy relaxation is found for short times. The theory has obvious applications to relaxation dynamics at ultra-short times as in observations on the femtosecond time scale and to the investigation of quantum coherence at those short times. While vibrational relaxation in chemical physics is a primary target of the study, another system of interest in condensed matter physics, an electron or hole in a lattice subjected to a strong DC electric field that gives rise to well-known Wannier-Stark ladders, is naturally addressed with the theory. Specific system-bath interactions are explored to obtain explicit details of the dynamics. General phenomenological descriptions of the reservoir are considered rather than specific microscopic realizations.
Al-Khalili, Jim
2003-01-01
In this lively look at quantum science, a physicist takes you on an entertaining and enlightening journey through the basics of subatomic physics. Along the way, he examines the paradox of quantum mechanics--beautifully mathematical in theory but confoundingly unpredictable in the real world. Marvel at the Dual Slit experiment as a tiny atom passes through two separate openings at the same time. Ponder the peculiar communication of quantum particles, which can remain in touch no matter how far apart. Join the genius jewel thief as he carries out a quantum measurement on a diamond without ever touching the object in question. Baffle yourself with the bizzareness of quantum tunneling, the equivalent of traveling partway up a hill, only to disappear then reappear traveling down the opposite side. With its clean, colorful layout and conversational tone, this text will hook you into the conundrum that is quantum mechanics.
Relaxation property of the fractional Brownian particle
International Nuclear Information System (INIS)
Wang Litan; Lung, C.W.
1988-08-01
Dynamic susceptibility of a diffusion system associated with the fractional Brownian motion (fBm) was examined for the fractal property of the Non-Debye relaxation process. The comparisons between fBm and other approaches were made. Anomalous diffusion and the Non-Debye relaxation processes were discussed with this approach. (author). 8 refs, 1 fig
Generalized Arcsine Laws for Fractional Brownian Motion.
Sadhu, Tridib; Delorme, Mathieu; Wiese, Kay Jörg
2018-01-26
The three arcsine laws for Brownian motion are a cornerstone of extreme-value statistics. For a Brownian B_{t} starting from the origin, and evolving during time T, one considers the following three observables: (i) the duration t_{+} the process is positive, (ii) the time t_{last} the process last visits the origin, and (iii) the time t_{max} when it achieves its maximum (or minimum). All three observables have the same cumulative probability distribution expressed as an arcsine function, thus the name arcsine laws. We show how these laws change for fractional Brownian motion X_{t}, a non-Markovian Gaussian process indexed by the Hurst exponent H. It generalizes standard Brownian motion (i.e., H=1/2). We obtain the three probabilities using a perturbative expansion in ϵ=H-1/2. While all three probabilities are different, this distinction can only be made at second order in ϵ. Our results are confirmed to high precision by extensive numerical simulations.
Brownian coagulation at high particle concentrations
Trzeciak, T.M.
2012-01-01
The process of Brownian coagulation, whereby particles are brought together by thermal motion and grow by collisions, is one of the most fundamental processes influencing the final properties of particulate matter in a variety of technically important systems. It is of importance in colloids,
A short walk in quantum probability
Hudson, Robin
2018-04-01
This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.
A short walk in quantum probability.
Hudson, Robin
2018-04-28
This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Quantum Chaos via the Quantum Action
Kröger, H.
2002-01-01
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincar\\'e sections obtained from the quantum action with those from the classical action.
International Nuclear Information System (INIS)
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.
2015-01-01
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Energy Technology Data Exchange (ETDEWEB)
Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)
2015-11-15
We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a
Chapter 5: Quantum Dynamics in Dissipative Molecular Systems
Zhang, Hou-Dao; Xu, J.; Xu, Rui-Xue; Yan, Y. J.
2014-04-01
The following sections are included: * Introduction * HEOM versus Path Integral Formalism: Background * Generic form and terminology of HEOM * Statistical mechanics description of bath influence * Feynman-Vernon influence functional formalism * General comments * Memory-Frequency Decomposition of Bath Correlation Functions * PSD of Bose function * Brownian oscillators decomposition of bath spectral density function * Optimized HEOM Theory With Accuracy Control * Construction of HEOM via path integral formalism * Accuracy control on white-noise residue ansatz * Efficient HEOM propagator: Numerical filtering and indexing algorithm * HEOM in Quantum Mechanics for Open Systems * The HEOM space and the Schrödinger picture * HEOM in the Heisenberg picture * Mixed Heisenberg-Schrödinger block-matrix dynamics in nonlinear optical response functions * Two-Dimensional Spectroscopy: Model Calculations * Concluding Remarks * Acknowledgments * References
Sarcan, F.; Nutku, F.; Donmez, O.; Kuruoglu, F.; Mutlu, S.; Erol, A.; Yildirim, S.; Arikan, M. C.
2015-08-01
We have performed magnetoresistance measurements on n- and p-type modulation doped GaInNAs/GaAs quantum well (QW) structures in both the weak (B magnetoresistance traces are used to extract the spin coherence, phase coherence and elastic scattering times as well Rashba parameters and spin-splitting energy. The calculated Rashba parameters for nitrogen containing samples reveal that the nitrogen composition is a significant parameter to determine the degree of the spin-orbit interactions. Consequently, GaInNAs-based QW structures with various nitrogen compositions can be beneficial to adjust the spin-orbit coupling strength and may be used as a candidate for spintronics applications.
International Nuclear Information System (INIS)
Oeiras, R. Y.; Silva, E. Z. da
2014-01-01
Carbon linear atomic chains attached to graphene have experimentally been produced. Motivated by these results, we study the nature of the carbon bonds in these nanowires and how it affects their electrical properties. In the present study we investigate chains with different numbers of atoms and we observe that nanowires with odd number of atoms present a distinct behavior than the ones with even numbers. Using graphene nanoribbons as leads, we identify differences in the quantum transport of the chains with the consequence that even and odd numbered chains have low and high electrical conduction, respectively. We also noted a dependence of current with the wire size. We study this unexpected behavior using a combination of first principles calculations and simple models based on chemical bond theory. From our studies, the electrons of carbon nanowires present a quasi-free electron behavior and this explains qualitatively the high electrical conduction and the bond lengths with unexpected values for the case of odd nanowires. Our study also allows the understanding of the electric conduction dependence with the number of atoms and their parity in the chain. In the case of odd number chains a proposed π-bond (MpB) model describes unsaturated carbons that introduce a mobile π-bond that changes dramatically the structure and transport properties of these wires. Our results indicate that the nature of bonds plays the main role in the oscillation of quantum electrical conduction for chains with even and odd number of atoms and also that nanowires bonded to graphene nanoribbons behave as a quasi-free electron system, suggesting that this behavior is general and it could also remain if the chains are bonded to other materials
Isotropic oscillator: spheroidal wave functions
International Nuclear Information System (INIS)
Mardoyan, L.G.; Pogosyan, G.S.; Ter-Antonyan, V.M.; Sisakyan, A.N.
1985-01-01
Solutions of the Schroedinger equation are found for an isotropic oscillator (10) in prolate and oblate spheroidal coordinates. It is shown that the obtained solutions turn into spherical and cylindrical bases of the isotropic oscillator at R→0 and R→ infinity (R is the dimensional parameter entering into the definition of prolate and oblate spheroidal coordinates). The explicit form is given for both prolate and oblate basis of the isotropic oscillator for the lowest quantum states
Brownian motion, martingales, and stochastic calculus
Le Gall, Jean-François
2016-01-01
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested i...
Fractional Brownian motion with a reflecting wall
Wada, Alexander H. O.; Vojta, Thomas
2018-02-01
Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of Monte Carlo simulations. Whereas the mean-square displacement of the particle shows the expected anomalous diffusion behavior ˜tα , the interplay between the geometric confinement and the long-time memory leads to a highly non-Gaussian probability density function with a power-law singularity at the barrier. In the superdiffusive case α >1 , the particles accumulate at the barrier leading to a divergence of the probability density. For subdiffusion α implications of these findings, in particular, for applications that are dominated by rare events.
Current fluctuations of interacting active Brownian particles
Pre, Trevor Grand; Limmer, David T.
2018-01-01
We derive the distribution function for particle currents for a system of interacting active Brownian particles in the long time limit using large deviation theory and a weighted many body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particle's orientation, and ...
Brownian motion, dynamical randomness and irreversibility
International Nuclear Information System (INIS)
Gaspard, Pierre
2005-01-01
A relationship giving the entropy production as the difference between a time-reversed entropy per unit time and the standard one is applied to stochastic processes of diffusion of Brownian particles between two reservoirs at different concentrations. The entropy production in the nonequilibrium steady state is interpreted in terms of a time asymmetry in the dynamical randomness between the forward and backward paths of the diffusion process
Brownian motion in short range random potentials
International Nuclear Information System (INIS)
Romero, A.H.; Romero, A.H.; Sancho, J.M.
1998-01-01
A numerical study of Brownian motion of noninteracting particles in random potentials is presented. The dynamics are modeled by Langevin equations in the high friction limit. The random potentials are Gaussian distributed and short ranged. The simulations are performed in one and two dimensions. Different dynamical regimes are found and explained. Effective subdiffusive exponents are obtained and commented on. copyright 1998 The American Physical Society
Frustrated Brownian Motion of Nonlocal Solitary Waves
International Nuclear Information System (INIS)
Folli, V.; Conti, C.
2010-01-01
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
Coldea, Amalia
FeSe is a unique and intriguing superconductor which can be tuned into a high temperature superconducting state using applied pressure, chemical intercalation and surface doping. In the absence of magnetism, the structural transition in FeSe is believed to be electronically driven, with the orbital degrees of freedom playing an important part. This scenario supports the stabilization of a nematic state in FeSe, which manifests as a Fermi surface deformation in the presence of strong interactions, as detected by ARPES. Another manifestation of the nematicity is the enhanced nematic susceptibility determined from elastoresistance measurements under applied strain. Isovalent Sulphur substitution onto the Selenium site constitutes a chemical pressure, which subtly modifies the electronic structure of FeSe, suppressing the structural transition without inducing high temperature superconductivity. I will present the evolution of the electronic structure with chemical pressure in FeSe, as determined from quantum oscillations and ARPES studies and I will discuss the suppression of the nematic electronic state and the role of electronic correlations. Experiments were performed at high magnetic field facilities in Tallahassee, Nijmegen and Toulouse and Diamond Light Source, UK. This work is mainly supported by EPSRC, UK (EP/I004475/1, EP/I017836/1) and I acknowledge my collaborators from Refs. .
Harrison, Neil; Shekhter, Arkady
2015-03-01
We investigate the origin of the small residual nodal bilayer-splitting in the underdoped high-Tc superconductor YBa2Cu3O6+x using the results of recently published angle-resolved quantum oscillation data [Sebastian et al., Nature 511, 61 (2014)]. A crucial clue to the origin of the residual bilayer-splitting is found to be provided by the anomalously small Zeeman-splitting of some of the observed cyclotron orbits. We show that such an anomalously Zeeman-splitting (or small effective g-factor) for a subset of orbits can be explained by spin-orbit interactions, which become significant in the nodal regions as a result of the vanishing bilayer coupling. The primary effect of spin-orbit interactions is to cause quasiparticles traversing the nodal region of the Brillouin zone to undergo a spin flip. We suggest that the Rashba-like spin-orbit interactions, naturally present in bilayer systems, have the right symmetry and magnitude to give rise to a network of coupled orbits consistent with experimental observations in underdoped YBa2Cu3O6+x. This work is supported by the DOEm BES proposal LANLF100, while the magnet lab is supported by the NSF and Florida State.
Rabanus, D; Graf, U U; Philipp, M; Ricken, O; Stutzki, J; Vowinkel, B; Wiedner, M C; Walther, C; Fischer, M; Faist, J
2009-02-02
We demonstrate for the first time the closure of an electronic phase lock loop for a continuous-wave quantum cascade laser (QCL) at 1.5 THz. The QCL is operated in a closed cycle cryo cooler. We achieved a frequency stability of better than 100 Hz, limited by the resolution bandwidth of the spectrum analyser. The PLL electronics make use of the intermediate frequency (IF) obtained from a hot electron bolometer (HEB) which is downconverted to a PLL IF of 125 MHz. The coarse selection of the longitudinal mode and the fine tuning is achieved via the bias voltage of the QCL. Within a QCL cavity mode, the free-running QCL shows frequency fluctuations of about 5 MHz, which the PLL circuit is able to control via the Stark-shift of the QCL gain material. Temperature dependent tuning is shown to be nonlinear, and of the order of -16 MHz/K. Additionally we have used the QCL as local oscillator (LO) to pump an HEB and perform, again for the first time at 1.5 THz, a heterodyne experiment, and obtain a receiver noise temperature of 1741 K.
Urkude, Rajashri; Rawat, Rajeev; Palikundwar, Umesh
2018-04-01
In 3D topological insulators, achieving a genuine bulk-insulating state is an important topic of research. The material system (Bi,Sb)2(Te,Se)3 has been proposed as a topological insulator with high resistivity and low carrier concentration. Topological insulators are predicted to present interesting surface transport phenomena but their experimental studies have been hindered by metallic bulk conduction that overwhelms the surface transport. Here we present a study of the bulk-insulating properties of (Bi0.3Sb0.7)2Te3. We show that a high resistivity exceeding 1 Ωm as a result of variable-range hopping behavior of state and Shubnikov-de Haas oscillations as coming from the topological surface state. We have been able to clarify both the bulk and surface transport channels, establishing a comprehensive understanding of the transport properties in this material. Our results demonstrate that (Bi0.3Sb0.7)2Te3 is a good material for studying the surface quantum transport in a topological insulator.
Pourret, Alexandre; Suzuki, Michi-To; Palaccio Morales, Alexandra; Seyfarth, Gabriel; Knebel, Georg; Aoki, Dai; Flouquet, Jacques
2017-08-01
The large quantum oscillations observed in the thermoelectric power in the antiferromagnetic (AF) state of the heavy-fermion compound CeRh2Si2 disappear suddenly when entering in the polarized paramagnetic (PPM) state at Hc ˜ 26.5 T, indicating an abrupt reconstruction of the Fermi surface. The electronic band structure was calculated using [LDA+U] for the AF state taking the correct magnetic structure into account, for the PPM state, and for the paramagnetic state (PM). Different Fermi surfaces were obtained for the AF, PM, and PPM states. Due to band folding, a large number of branches was expected and observed in the AF state. The LDA+U calculation was compared with the previous LDA calculations. Furthermore, we compared both calculations with previously published de Haas-van Alphen experiments. The better agreement with the LDA approach suggests that above the critical pressure pc CeRh2Si2 enters in a mixed-valence state. In the PPM state under a high magnetic field, the 4f contribution at the Fermi level EF drops significantly compared with that in the PM state, and the 4f electrons contribute only weakly to the Fermi surface in our approach.
Optimum analysis of a Brownian refrigerator.
Luo, X G; Liu, N; He, J Z
2013-02-01
A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.
Analyzing animal movements using Brownian bridges.
Horne, Jon S; Garton, Edward O; Krone, Stephen M; Lewis, Jesse S
2007-09-01
By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.
Intrinsic and extrinsic measurement for Brownian motion
International Nuclear Information System (INIS)
Castro-Villarreal, Pavel
2014-01-01
Based upon the Smoluchowski equation on curved manifolds, three physical observables are considered for Brownian displacement, namely geodesic displacement s, Euclidean displacement δR, and projected displacement δR ⊥ . The Weingarten–Gauss equations are used to calculate the mean-square Euclidean displacements in the short-time regime. Our findings show that from an extrinsic point of view the geometry of the space affects the Brownian motion in such a way that the particle’s diffusion is decelerated, contrasting with the intrinsic point of view where dynamics is controlled by the sign of the Gaussian curvature (Castro-Villarreal, 2010 J. Stat. Mech. P08006). Furthermore, it is possible to give exact formulas for 〈δR〉 and 〈δR 2 〉 on spheres and minimal surfaces, which are valid for all values of time. In the latter case, surprisingly, Brownian motion corresponds to the usual diffusion in flat geometries, albeit minimal surfaces have non-zero Gaussian curvature. Finally, the two-dimensional case is emphasized due to its close relation to surface self-diffusion in fluid membranes. (paper)
Interacting Brownian Swarms: Some Analytical Results
Directory of Open Access Journals (Sweden)
Guillaume Sartoretti
2016-01-01
Full Text Available We consider the dynamics of swarms of scalar Brownian agents subject to local imitation mechanisms implemented using mutual rank-based interactions. For appropriate values of the underlying control parameters, the swarm propagates tightly and the distances separating successive agents are iid exponential random variables. Implicitly, the implementation of rank-based mutual interactions, requires that agents have infinite interaction ranges. Using the probabilistic size of the swarm’s support, we analytically estimate the critical interaction range below that flocked swarms cannot survive. In the second part of the paper, we consider the interactions between two flocked swarms of Brownian agents with finite interaction ranges. Both swarms travel with different barycentric velocities, and agents from both swarms indifferently interact with each other. For appropriate initial configurations, both swarms eventually collide (i.e., all agents interact. Depending on the values of the control parameters, one of the following patterns emerges after collision: (i Both swarms remain essentially flocked, or (ii the swarms become ultimately quasi-free and recover their nominal barycentric speeds. We derive a set of analytical flocking conditions based on the generalized rank-based Brownian motion. An extensive set of numerical simulations corroborates our analytical findings.
Properties of Brownian Image Models in Scale-Space
DEFF Research Database (Denmark)
Pedersen, Kim Steenstrup
2003-01-01
Brownian images) will be discussed in relation to linear scale-space theory, and it will be shown empirically that the second order statistics of natural images mapped into jet space may, within some scale interval, be modeled by the Brownian image model. This is consistent with the 1/f 2 power spectrum...... law that apparently governs natural images. Furthermore, the distribution of Brownian images mapped into jet space is Gaussian and an analytical expression can be derived for the covariance matrix of Brownian images in jet space. This matrix is also a good approximation of the covariance matrix......In this paper it is argued that the Brownian image model is the least committed, scale invariant, statistical image model which describes the second order statistics of natural images. Various properties of three different types of Gaussian image models (white noise, Brownian and fractional...
Harmonic oscillator in Snyder space
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
Time rescaling and Gaussian properties of the fractional Brownian motions
International Nuclear Information System (INIS)
Maccone, C.
1981-01-01
The fractional Brownian motions are proved to be a class of Gaussian (normal) stochastic processes suitably rescaled in time. Some consequences affecting their eigenfunction expansion (Karhunen-Loeve expansion) are inferred. A known formula of Cameron and Martin is generalized. The first-passage time probability density is found. The partial differential equation of the fractional Brownian diffusion is obtained. And finally the increments of the fractional Brownian motions are proved to be independent for nonoverlapping time intervals. (author)
International Nuclear Information System (INIS)
Plyukhin, A.V.
2013-01-01
A model of an autonomous isothermal Brownian motor with an internal propulsion mechanism is considered. The motor is a Brownian particle which is semi-transparent for molecules of surrounding ideal gas. Molecular passage through the particle is controlled by a potential similar to that in the transition rate theory, i.e. characterized by two stationary states with a finite energy difference separated by a potential barrier. The internal potential drop maintains the diode-like asymmetry of molecular fluxes through the particle, which results in the particle's stationary drift.
Quantum dynamics of quantum bits
International Nuclear Information System (INIS)
Nguyen, Bich Ha
2011-01-01
The theory of coherent oscillations of the matrix elements of the density matrix of the two-state system as a quantum bit is presented. Different calculation methods are elaborated in the case of a free quantum bit. Then the most appropriate methods are applied to the study of the density matrices of the quantum bits interacting with a classical pumping radiation field as well as with the quantum electromagnetic field in a single-mode microcavity. The theory of decoherence of a quantum bit in Markovian approximation is presented. The decoherence of a quantum bit interacting with monoenergetic photons in a microcavity is also discussed. The content of the present work can be considered as an introduction to the study of the quantum dynamics of quantum bits. (review)
Langevin theory of anomalous Brownian motion made simple
International Nuclear Information System (INIS)
Tothova, Jana; Vasziova, Gabriela; Lisy, VladimIr; Glod, Lukas
2011-01-01
During the century from the publication of the work by Einstein (1905 Ann. Phys. 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 C. R. Acad. Sci., Paris 146 530), in which he proposed an 'infinitely more simple' description of Brownian motion than that by Einstein. The original Langevin approach has however strong limitations, which were rigorously stated after the creation of the hydrodynamic theory of Brownian motion (1945). Hydrodynamic Brownian motion is a special case of 'anomalous Brownian motion', now intensively studied both theoretically and in experiments. We show how some general properties of anomalous Brownian motion can be easily derived using an effective method that allows one to convert the stochastic generalized Langevin equation into a deterministic Volterra-type integro-differential equation for the mean square displacement of the particle. Within the Gibbs statistics, the method is applicable to linear equations of motion with any kind of memory during the evolution of the system. We apply it to memoryless Brownian motion in a harmonic potential well and to Brownian motion in fluids, taking into account the effects of hydrodynamic memory. Exploring the mathematical analogy between Brownian motion and electric circuits, which are at nanoscales also described by the generalized Langevin equation, we calculate the fluctuations of charge and current in RLC circuits that are in contact with the thermal bath. Due to the simplicity of our approach it could be incorporated into graduate courses of statistical physics. Once the method is established, it allows bringing to the attention of students and effectively solving a number of attractive problems related to Brownian motion.
International Nuclear Information System (INIS)
Okuyama, Kikuo; Kousaka, Yasuo; Yoshida, Tetsuo
1976-01-01
The behavior of aerosols undergoing Brownian coagulation. Brownian diffusion and gravitational settling in a closed chamber was studied by solving the basic equation, the so-called population balance equation, numerically for a polydisperse aerosol system and analytically for a monodisperse system, and then the results were examined by experiment. In solving the basic equation, two dimensionless parameters, which are determined by the initial properties of an aerosol and the chamber dimension and also characterize the relative effects of Brownian coagulation and Brownian diffusion to gravitational settling, were introduced in order to generalize the behavior under arbitrary conditions. The calculated results, the time-dependent changes in particle number concentration and particle size distribution for a polydisperse system, were presented graphically by using the above two parameters. And further using these parameters, the domains of the three controlling factors were mapped to show the extent of each effect of these factors under various conditions for a monodisperse system. Some of the calculated results were compared with the experimental results obtained by the ultramicroscopic size analysis previously developed by the authors. (auth.)
The relativistic Brownian motion: Interdisciplinary applications
International Nuclear Information System (INIS)
Aragones-Munoz, A; Sandoval-Villalbazo, A
2010-01-01
Relativistic Brownian motion theory will be applied to the study of analogies between physical and economic systems, emphasizing limiting cases in which Gaussian distributions are no longer valid. The characteristic temperatures of the particles will be associated with the concept of variance, and this will allow us to choose whether the pertinent distribution is classical or relativistic, while working specific situations. The properties of particles can be interpreted as economic variables, in order to study the behavior of markets in terms of Levy financial processes, since markets behave as stochastic systems. As far as we know, the application of the Juettner distribution to the study of economic systems is a new idea.
Effective diffusion of confined active Brownian swimmers
Sandoval, Mario; Dagdug, Leonardo
2014-11-01
We find theoretically the effect of confinement and thermal fluctuations, on the diffusivity of a spherical active swimmer moving inside a two-dimensional narrow cavity of general shape. The explicit formulas for the effective diffusion coefficient of a swimmer moving inside two particular cavities are presented. We also compare our analytical results with Brownian Dynamics simulations and we obtain excellent agreement. L.D. thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) Mexico, for partial support by Grant No. 176452. M. S. thanks CONACyT and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work under Grant No. 103.5/13/6732.
Eigenfunction statistics of Wishart Brownian ensembles
International Nuclear Information System (INIS)
Shukla, Pragya
2017-01-01
We theoretically analyze the eigenfunction fluctuation measures for a Hermitian ensemble which appears as an intermediate state of the perturbation of a stationary ensemble by another stationary ensemble of Wishart (Laguerre) type. Similar to the perturbation by a Gaussian stationary ensemble, the measures undergo a diffusive dynamics in terms of the perturbation parameter but the energy-dependence of the fluctuations is different in the two cases. This may have important consequences for the eigenfunction dynamics as well as phase transition studies in many areas of complexity where Brownian ensembles appear. (paper)
Laser light scattering in Brownian medium
International Nuclear Information System (INIS)
Suwono; Santoso, Budi; Baiquni, A.
1983-01-01
The principle of laser light scattering in Brownian medium and photon correlation spectroscopy are described in detail. Their application to the study of the behaviour of a polystyrene latex solution are discussed. The auto-correlation function of light scattered by the polystyrene latex solution in various angle, various temperature and in various sample times, have been measured. Information on the translation diffusion coefficient and size on the particle can be obtained from the auto-correlation function. Good agreement between the available data and experiment is shown. (author)
Quantum ratchets reroute electrons
International Nuclear Information System (INIS)
Haenggi, P.; Reimann, P.
1999-01-01
Is it possible to extract energy from random fluctuations and put it to use? This challenging question has provoked discussion ever since the early days of Brownian-motion theory. For large-scale or macroscopic fluctuations, the answer is ''yes'' - the principle is demonstrated, for example, in the self-winding wristwatch. Much subtler is the issue of whether microscopic random fluctuations, such as thermal Brownian motion or even the haphazard motion of quantum particles, acting as a random energy source can cause the particles to flow in one direction only. In recent years this field has been the scene of remarkable activity, motivated by the prospect of potentially high-profile technological and biological applications, such as molecular motors. In particular the directed transport of particles in an asymmetric potential known as a ratchet has received a lot of attention. This research, however, has focused on ''thermal ratchets'' in which the particles undergo thermal Brownian motion: the next challenge is to move from the classical world and account for quantum mechanical effects. Recently a collaboration between physicists at Lund University in Sweden and the Niels Bohr Institute in Copenhagen has taken a significant step forward and built a quantum ratchet (H Linke et al. 1998 Europhys. Lett. 44 341 and 45 406). The device is based on an aluminium-doped gallium arsenide (GaAs/AlGaAs) quantum dot with a ratchet-like, triangular-shaped cavity. In this article the authors discuss the implications of this work. (UK)
Diffusion in one dimensional random medium and hyperbolic Brownian motion
International Nuclear Information System (INIS)
Comtet, A.; Monthus, C.; Paris-6 Univ., 75
1995-03-01
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. This relationship is analyzed in detail and various distributions are studied using stochastic calculus and functional integration. (author) 17 refs
Simple Brownian diffusion an introduction to the standard theoretical models
Gillespie, Daniel T
2013-01-01
Brownian diffusion, the motion of large molecules in a sea of very many much smaller molecules, is topical because it is one of the ways in which biologically important molecules move about inside living cells. This book presents the mathematical physics that underlies the four simplest models of Brownian diffusion.
Self-induced temperature gradients in Brownian dynamics
Devine, Jack; Jack, M. W.
2017-12-01
Brownian systems often surmount energy barriers by absorbing and emitting heat to and from their local environment. Usually, the temperature gradients created by this heat exchange are assumed to dissipate instantaneously. Here we relax this assumption to consider the case where Brownian dynamics on a time-independent potential can lead to self-induced temperature gradients. In the same way that externally imposed temperature gradients can cause directed motion, these self-induced gradients affect the dynamics of the Brownian system. The result is a coupling between the local environment and the Brownian subsystem. We explore the resulting dynamics and thermodynamics of these coupled systems and develop a robust method for numerical simulation. In particular, by focusing on one-dimensional situations, we show that self-induced temperature gradients reduce barrier-crossing rates. We also consider a heat engine and a heat pump based on temperature gradients induced by a Brownian system in a nonequilibrium potential.
Langevin formulation of quantum dynamics
International Nuclear Information System (INIS)
Roncadelli, M.
1989-03-01
We first show that nonrelativistic quantum mechanics formulated at imaginary-(h/2 π) can formally be viewed as the Fokker-Planck description of a frictionless brownian motion, which occurs (in general) in an absorbing medium. We next offer a new formulation of quantum mechanics, which is basically the Langevin treatment of this brownian motion. Explicitly, we derive a noise-average representation for the transition probability W(X'',t''|X',t'), in terms of the solutions to a Langevin equation with a Gaussian white-noise. Upon analytic continuation back to real-(h/2 π),W(X'',t''|X',t') becomes the propagator of the original Schroedinger equation. Our approach allows for a straightforward application to quantum dynamical problems of the mathematical techniques of classical stochastic processes. Moreover, computer simulations of quantum mechanical systems can be carried out by using numerical programs based on the Langevin dynamics. (author). 19 refs, 1 tab
Two derivations of the master equation of quantum Brownian motion
Energy Technology Data Exchange (ETDEWEB)
Halliwell, J J [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
2007-03-23
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model.
Two derivations of the master equation of quantum Brownian motion
International Nuclear Information System (INIS)
Halliwell, J J
2007-01-01
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model
International Nuclear Information System (INIS)
Greczylo, Tomasz; Debowska, Ewa
2007-01-01
The authors make comments and remarks on the papers by Salmon et al (2002 Eur. J. Phys. 23 249-53) and their own (2005 Eur. J. Phys. 26 827-33) concerning Brownian motion in two-dimensional space. New, corrected results of calculations and measurements for students' experiments on finding the viscosity of liquids from Brownian motion are presented. (letters and comments)
Quantum dissipative systems from theory of continuous measurements
International Nuclear Information System (INIS)
Mensky, Michael B.; Stenholm, Stig
2003-01-01
We apply the restricted-path-integral (RPI) theory of non-minimally disturbing continuous measurements for correct description of frictional Brownian motion. The resulting master equation is automatically of the Lindblad form, so that the difficulties typical of other approaches do not exist. In the special case of harmonic oscillator the known familiar master equation describing its frictionally driven Brownian motion is obtained. A thermal reservoir as a measuring environment is considered
Entanglement in neutrino oscillations
Energy Technology Data Exchange (ETDEWEB)
Blasone, M.; Dell' Anno, F.; De Siena, S.; Illuminati, F. [Universita degli Studi di Salerno Via Ponte don Melillon, Dipt. di Matematica e Informatica, Fisciano SA (Italy); INFN Sezione di Napoli, Gruppo collegato di Salerno - Baronissi SA (Italy); Dell' Anno, F.; De Siena, S.; Illuminati, F. [CNR-INFM Coherentia - Napoli (Italy); Blasone, M. [ISI Foundation for Scientific Interchange, Torino (Italy)
2009-03-15
Flavor oscillations in elementary particle physics are related to multimode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks. (authors)
Entanglement in neutrino oscillations
International Nuclear Information System (INIS)
Blasone, M.; Dell'Anno, F.; De Siena, S.; Illuminati, F.; Dell'Anno, F.; De Siena, S.; Illuminati, F.; Blasone, M.
2009-01-01
Flavor oscillations in elementary particle physics are related to multimode entanglement of single-particle states. We show that mode entanglement can be expressed in terms of flavor transition probabilities, and therefore that single-particle entangled states acquire a precise operational characterization in the context of particle mixing. We treat in detail the physically relevant cases of two- and three-flavor neutrino oscillations, including the effective measure of CP violation. We discuss experimental schemes for the transfer of the quantum information encoded in single-neutrino states to spatially delocalized two-flavor charged-lepton states, thus showing, at least in principle, that single-particle entangled states of neutrino mixing are legitimate physical resources for quantum information tasks. (authors)
Neutrino Masses and Oscillations
CERN. Geneva. Audiovisual Unit; Treille, Daniel
2002-01-01
This course will not cover its subject in the customary way. The emphasis will be on the simple theoretical concepts (helicity, handedness, chirality, Majorana masses) which are obscure in most of the literature, and on the quantum mechanics of oscillations, that ALL books get wrong. Which, hopefully, will not deter me from discussing some of the most interesting results from the labs and from the cosmos.
Development and Application of Semiconductor Quantum Dots to Quantum Computing
National Research Council Canada - National Science Library
Steel, Duncan
2002-01-01
.... Several major milestones were achieved during the present program including the demonstration of optically induced and detected quantum entanglement of two qubits, Rabi oscillation (one bit rotation...
Directed motion of a Brownian motor in a temperature gradient
Liu, Yibing; Nie, Wenjie; Lan, Yueheng
2017-05-01
Directed motion of mesoscopic systems in a non-equilibrium environment is of great interest to both scientists and engineers. Here, the translation and rotation of a Brownian motor is investigated under non-equilibrium conditions. An anomalous directed translation is found if the two heads of the Brownian motor are immersed in baths with different particle masses, which is hinted in the analytic computation and confirmed by the numerical simulation. Similar consideration is also used to find the directed movement in the single rotational and translational degree of freedom of the Brownian motor when residing in one thermal bath with a temperature gradient.
Brownian motion probe for water-ethanol inhomogeneous mixtures
Furukawa, Kazuki; Judai, Ken
2017-12-01
Brownian motion provides information regarding the microscopic geometry and motion of molecules, insofar as it occurs as a result of molecular collisions with a colloid particle. We found that the mobility of polystyrene beads from the Brownian motion in a water-ethanol mixture is larger than that predicted from the liquid shear viscosity. This indicates that mixing water and ethanol is inhomogeneous in micron-sized probe beads. The discrepancy between the mobility of Brownian motion and liquid mobility can be explained by the way the rotation of the beads in an inhomogeneous viscous solvent converts the translational movement.
Fractional Brownian motion and long term clinical trial recruitment.
Zhang, Qiang; Lai, Dejian
2011-05-01
Prediction of recruitment in clinical trials has been a challenging task. Many methods have been studied, including models based on Poisson process and its large sample approximation by Brownian motion (BM), however, when the independent incremental structure is violated for BM model, we could use fractional Brownian motion to model and approximate the underlying Poisson processes with random rates. In this paper, fractional Brownian motion (FBM) is considered for such conditions and compared to BM model with illustrated examples from different trials and simulations.
Conformal geometry and invariants of 3-strand Brownian braids
International Nuclear Information System (INIS)
Nechaev, Sergei; Voituriez, Raphael
2005-01-01
We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the properties of conformal maps of doubly-punctured plane z to the universal covering surface. The special attention is paid to the case of indistinguishable particles. Our method of conformal maps allows us to investigate the statistical properties of the topological complexity of a bunch of 3-strand Brownian braids and to compute the expectation value of the irreducible braid length in the non-Abelian case
Breaking the symmetry of a Brownian motor with symmetric potentials
International Nuclear Information System (INIS)
Hagman, H; Zelan, M; Dion, C M
2011-01-01
The directed transport of Brownian particles requires a system with an asymmetry and with non-equilibrium noise. Here we investigate numerically alternative ways of fulfilling these requirements for a two-state Brownian motor, realized with Brownian particles alternating between two phase-shifted, symmetric potentials. We show that, besides the previously known spatio-temporal asymmetry based on unequal transfer rates between the potentials, inequalities in the potential depths, the frictions, or the equilibrium temperatures of the two potentials also generate the required asymmetry. We also show that the effects of the thermal noise and the noise of the transfer's randomness depend on the way the asymmetry is induced.
Parallel Molecular Distributed Detection With Brownian Motion.
Rogers, Uri; Koh, Min-Sung
2016-12-01
This paper explores the in vivo distributed detection of an undesired biological agent's (BAs) biomarkers by a group of biological sized nanomachines in an aqueous medium under drift. The term distributed, indicates that the system information relative to the BAs presence is dispersed across the collection of nanomachines, where each nanomachine possesses limited communication, computation, and movement capabilities. Using Brownian motion with drift, a probabilistic detection and optimal data fusion framework, coined molecular distributed detection, will be introduced that combines theory from both molecular communication and distributed detection. Using the optimal data fusion framework as a guide, simulation indicates that a sub-optimal fusion method exists, allowing for a significant reduction in implementation complexity while retaining BA detection accuracy.
Communication: Memory effects and active Brownian diffusion
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Pulak K. [Department of Chemistry, Presidency University, Kolkata 700073 (India); Li, Yunyun, E-mail: yunyunli@tongji.edu.cn [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Marchegiani, Giampiero [Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Marchesoni, Fabio [Center for Phononics and Thermal Energy Science, Tongji University, Shanghai 200092 (China); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy)
2015-12-07
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal noise, its angular randomization is described as a memoryless stochastic process. Here, we speculate that finite-time correlations in the orientational dynamics can affect the swimmer’s diffusivity. To this purpose, we propose and solve two alternative models. In the first one, we simply assume that the environmental fluctuations governing the swimmer’s propulsion are exponentially correlated in time, whereas in the second one, we account for possible damped fluctuations of the propulsion velocity around the swimmer’s axis. The corresponding swimmer’s diffusion constants are predicted to get, respectively, enhanced or suppressed upon increasing the model memory time. Possible consequences of this effect on the interpretation of the experimental data are discussed.
Brownian Motion of Boomerang Colloidal Particles
Wei, Qi-Huo; Konya, Andrew; Wang, Feng; Selinger, Jonathan V.; Sun, Kai; Chakrabarty, Ayan
2014-03-01
We present experimental and theoretical studies on the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.
Brownian motion with multiplicative noises revisited
International Nuclear Information System (INIS)
Kuroiwa, T; Miyazaki, K
2014-01-01
The Langevin equation with multiplicative noise and a state-dependent transport coefficient should always complemented with the proper interpretation rule of the noise, such as the Itô and Stratonovich conventions. Although the mathematical relationship between the different rules and how to translate from one rule to another are well established, the subject of which is a more physically natural rule still remains controversial. In this communication, we derive the overdamped Langevin equation with multiplicative noise for Brownian particles, by systematically eliminating the fast degrees of freedom of the underdamped Langevin equation. The Langevin equations obtained here vary depending on the choice of the noise conventions but they are different representations for an identical phenomenon. The results apply to multi-variable, nonequilibrium, non-stationary systems, and other general settings. (fast track communication)
Factorization Procedure for Harmonically Bound Brownian Particle
International Nuclear Information System (INIS)
Omolo, JK.
2006-01-01
The method of factorization to solve the problem of the one-dimensional harmonically bound Brownian particle was applied. Assuming the the rapidily fluctuating random force is Gaussian and has an infinitely short correlation time, explicit expressions for the position-position,velocity-velocity, and the position-velocity correlation functions, which are also use to write down appropriate distribution functions were used. The correlation and distribution functions for the complex quantity (amplititude) which provides the expressions for the position and velocity of the particle are calculated. Finally, Fokker-Planck equations for the joint probability distribution functions for the amplititude and it's complex conjugate as well as for the position and velocity of the particle are obtained. (author)
Yukawa Potential, Panharmonic Measure and Brownian Motion
Directory of Open Access Journals (Sweden)
Antti Rasila
2018-05-01
Full Text Available This paper continues our earlier investigation, where a walk-on-spheres (WOS algorithm for Monte Carlo simulation of the solutions of the Yukawa and the Helmholtz partial differential equations (PDEs was developed by using the Duffin correspondence. In this paper, we investigate the foundations behind the algorithm for the case of the Yukawa PDE. We study the panharmonic measure, which is a generalization of the harmonic measure for the Yukawa PDE. We show that there are natural stochastic definitions for the panharmonic measure in terms of the Brownian motion and that the harmonic and the panharmonic measures are all mutually equivalent. Furthermore, we calculate their Radon–Nikodym derivatives explicitly for some balls, which is a key result behind the WOS algorithm.
International Nuclear Information System (INIS)
McNeill, G.A.
1981-01-01
Present high-speed data acquisition systems in nuclear diagnostics use high-frequency oscillators to provide timing references for signals recorded on fast, traveling-wave oscilloscopes. An oscillator's sinusoidal wave shape is superimposed on the recorded signal with each cycle representing a fixed time increment. During data analysis the sinusoid is stripped from the signal, leaving a clean signal shape with known timing. Since all signal/time relationships are totally dependant upon working oscillators, these critical devices must have remote verification of proper operation. This manual presents the newly-developed oscillator monitor which will provide the required verification
Conformal correlation functions in the Brownian loop soup
Camia, Federico; Gandolfi, Alberto; Kleban, Matthew
2016-01-01
We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.
Conformal correlation functions in the Brownian loop soup
Energy Technology Data Exchange (ETDEWEB)
Camia, Federico, E-mail: federico.camia@nyu.edu [New York University Abu Dhabi (United Arab Emirates); VU University, Amsterdam (Netherlands); Gandolfi, Alberto, E-mail: albertogandolfi@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Università di Firenze (Italy); Kleban, Matthew, E-mail: kleban@nyu.edu [New York University Abu Dhabi (United Arab Emirates); Center for Cosmology and Particle Physics, Department of Physics, New York University (United States)
2016-01-15
We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point) in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.
Conformal correlation functions in the Brownian loop soup
Directory of Open Access Journals (Sweden)
Federico Camia
2016-01-01
Full Text Available We define and study a set of operators that compute statistical properties of the Brownian loop soup, a conformally invariant gas of random Brownian loops (Brownian paths constrained to begin and end at the same point in two dimensions. We prove that the correlation functions of these operators have many of the properties of conformal primaries in a conformal field theory, and compute their conformal dimension. The dimensions are real and positive, but have the novel feature that they vary continuously as a periodic function of a real parameter. We comment on the relation of the Brownian loop soup to the free field, and use this relation to establish that the central charge of the loop soup is twice its intensity.
An explicit local uniform large deviation bound for Brownian bridges
Wittich, O.
2005-01-01
By comparing curve length in a manifold and a standard sphere, we prove a local uniform bound for the exponent in the Large Deviation formula that describes the concentration of Brownian bridges to geodesics.
Near-Field, On-Chip Optical Brownian Ratchets.
Wu, Shao-Hua; Huang, Ningfeng; Jaquay, Eric; Povinelli, Michelle L
2016-08-10
Nanoparticles in aqueous solution are subject to collisions with solvent molecules, resulting in random, Brownian motion. By breaking the spatiotemporal symmetry of the system, the motion can be rectified. In nature, Brownian ratchets leverage thermal fluctuations to provide directional motion of proteins and enzymes. In man-made systems, Brownian ratchets have been used for nanoparticle sorting and manipulation. Implementations based on optical traps provide a high degree of tunability along with precise spatiotemporal control. Here, we demonstrate an optical Brownian ratchet based on the near-field traps of an asymmetrically patterned photonic crystal. The system yields over 25 times greater trap stiffness than conventional optical tweezers. Our technique opens up new possibilities for particle manipulation in a microfluidic, lab-on-chip environment.
From a stochastic to a macroscopic approach to brownian motion
International Nuclear Information System (INIS)
Bocquet, L.
1998-01-01
In this lecture, we examine the dynamics of suspensions of mesoscopic (Brownian) particles in a molecular fluid, starting from first principles. We introduce the technique of multiple time-scales to derive the Fokker-Planck equation for a single, or for a set of interacting Brownian particles, starting from the Liouville equation for the full system (Brownian particles and discrete bath). The limitations of the Fokker-Planck equation will then be emphasized. In particular, we shall point out that under ''standard'' experimental conditions, the Fokker-Planck description cannot be correct and that non-Markovian effects are expected. A microscopic description in the true experimental limit confirms this breakdown and leads to a ''generalized'' (non-Markovian and non-local in velocity space) Fokker-Planck equation, which describes the thermalization of the Brownian particle. (author)
Directed Transport of Brownian Particles in a Periodic Channel
International Nuclear Information System (INIS)
Jiang Jie; Ai Bao-Quan; Wu Jian-Chun
2015-01-01
The transport of Brownian particles in the infinite channel within an external force along the axis of the channel has been studied. In this paper, we study the transport of Brownian particle in the infinite channel within an external force along the axis of the channel and an external force in the transversal direction. In this more sophisticated situation, some property is similar to the simple situation, but some interesting property also appears. (paper)
Volume of the domain visited by N spherical Brownian particles
International Nuclear Information System (INIS)
Berezhkovskii, A.M.
1994-01-01
The average value and variance of the volume of the domain visited in time t by N spherical Brownian particles starting initially at the same point are presented as quadratures of the solutions of simple diffusion problems of the survival of a point Brownian particle in the presence of one and two spherical traps. As an illustration, explicit time dependences are obtained for the average volume in one and three dimensions
Fast orthogonal transforms and generation of Brownian paths.
Leobacher, Gunther
2012-04-01
We present a number of fast constructions of discrete Brownian paths that can be used as alternatives to principal component analysis and Brownian bridge for stratified Monte Carlo and quasi-Monte Carlo. By fast we mean that a path of length [Formula: see text] can be generated in [Formula: see text] floating point operations. We highlight some of the connections between the different constructions and we provide some numerical examples.
Estimation of the global regularity of a multifractional Brownian motion
DEFF Research Database (Denmark)
Lebovits, Joachim; Podolskij, Mark
This paper presents a new estimator of the global regularity index of a multifractional Brownian motion. Our estimation method is based upon a ratio statistic, which compares the realized global quadratic variation of a multifractional Brownian motion at two different frequencies. We show that a ...... that a logarithmic transformation of this statistic converges in probability to the minimum of the Hurst functional parameter, which is, under weak assumptions, identical to the global regularity index of the path....
Damped Oscillator with Delta-Kicked Frequency
Manko, O. V.
1996-01-01
Exact solutions of the Schrodinger equation for quantum damped oscillator subject to frequency delta-kick describing squeezed states are obtained. The cases of strong, intermediate, and weak damping are investigated.
Correlational approach to study interactions between dust Brownian particles in a plasma
Lisin, E. A.; Vaulina, O. S.; Petrov, O. F.
2018-01-01
A general approach to the correlational analysis of Brownian motion of strongly coupled particles in open dissipative systems is described. This approach can be applied to the theoretical description of various non-ideal statistically equilibrium systems (including non-Hamiltonian systems), as well as for the analysis of experimental data. In this paper, we consider an application of the correlational approach to the problem of experimental exploring the wake-mediated nonreciprocal interactions in complex plasmas. We derive simple analytic equations, which allows one to calculate the gradients of forces acting on a microparticle due to each of other particles as well as the gradients of external field, knowing only the information on time-averaged correlations of particles displacements and velocities. We show the importance of taking dissipative and random processes into account, without which consideration of a system with a nonreciprocal interparticle interaction as linearly coupled oscillators leads to significant errors in determining the characteristic frequencies in a system. In the examples of numerical simulations, we demonstrate that the proposed original approach could be an effective instrument in exploring the longitudinal wake structure of a microparticle in a plasma. Unlike the previous attempts to study the wake-mediated interactions in complex plasmas, our method does not require any external perturbations and is based on Brownian motion analysis only.
Lites, B.W.; Rutten, R.J.; Thomas, J.H.
1995-01-01
We show results from SO/Sacramento Peak data to discuss three issues: (i)--the spatial occurrence of chromospheric 3--min oscillations; (ii)--the validity of Ca II H&K line-center Doppler Shift measurements; (iii)--the signi ?cance of oscillation power and phase at frequencies above 10 mHz.
Wave Physics Oscillations - Solitons - Chaos
Nettel, Stephen
2009-01-01
This textbook is intended for those second year undergraduates in science and engineering who will later need an understanding of electromagnetic theory and quantum mechanics. The classical physics of oscillations and waves is developed at a more advanced level than has been customary for the second year, providing a basis for the quantum mechanics that follows. In this new edition the Green's function is explained, reinforcing the integration of quantum mechanics with classical physics. The text may also form the basis of an "introduction to theoretical physics" for physics majors. The concluding chapters give special attention to topics in current wave physics: nonlinear waves, solitons, and chaotic behavior.
Ellipsoidal basis for isotropic oscillator
International Nuclear Information System (INIS)
Kallies, W.; Lukac, I.; Pogosyan, G.S.; Sisakyan, A.N.
1994-01-01
The solutions of the Schroedinger equation are derived for the isotropic oscillator potential in the ellipsoidal coordinate system. The explicit expression is obtained for the ellipsoidal integrals of motion through the components of the orbital moment and Demkov's tensor. The explicit form of the ellipsoidal basis is given for the lowest quantum numbers. 10 refs.; 1 tab. (author)
International Nuclear Information System (INIS)
Radiom, Milad; Ducker, William; Robbins, Brian; Paul, Mark
2015-01-01
The hydrodynamic interaction of two closely spaced micron-scale spheres undergoing Brownian motion was measured as a function of their separation. Each sphere was attached to the distal end of a different atomic force microscopy cantilever, placing each sphere in a stiff one-dimensional potential (0.08 Nm −1 ) with a high frequency of thermal oscillations (resonance at 4 kHz). As a result, the sphere’s inertial and restoring forces were significant when compared to the force due to viscous drag. We explored interparticle gap regions where there was overlap between the two Stokes layers surrounding each sphere. Our experimental measurements are the first of their kind in this parameter regime. The high frequency of oscillation of the spheres means that an analysis of the fluid dynamics would include the effects of fluid inertia, as described by the unsteady Stokes equation. However, we find that, for interparticle separations less than twice the thickness of the wake of the unsteady viscous boundary layer (the Stokes layer), the hydrodynamic interaction between the Brownian particles is well-approximated by analytical expressions that neglect the inertia of the fluid. This is because elevated frictional forces at narrow gaps dominate fluid inertial effects. The significance is that interparticle collisions and concentrated suspensions at this condition can be modeled without the need to incorporate fluid inertia. We suggest a way to predict when fluid inertial effects can be ignored by including the gap-width dependence into the frequency number. We also show that low frequency number analysis can be used to determine the microrheology of mixtures at interfaces
Brownian dynamics simulations of insulin microspheres formation
Li, Wei; Chakrabarti, Amit; Gunton, James
2010-03-01
Recent experiments have indicated a novel, aqueous process of microsphere insulin fabrication based on controlled phase separation of protein from water-soluble polymers. We investigate the insulin microsphere crystal formation from insulin-PEG-water systems via 3D Brownian Dynamics simulations. We use the two component Asakura-Oosawa model to simulate the kinetics of this colloid polymer mixture. We first perform a deep quench below the liquid-crystal boundary that leads to fractal formation. We next heat the system to obtain a break-up of the fractal clusters and subsequently cool the system to obtain a spherical aggregation of droplets with a relatively narrow size distribution. We analyze the structure factor S(q) to identify the cluster dimension. S(q) crosses over from a power law q dependence of 1.8 (in agreement with DLCA) to 4 as q increases, which shows the evolution from fractal to spherical clusters. By studying the bond-order parameters, we find the phase transition from liquid-like droplets to crystals which exhibit local HCP and FCC order. This work is supported by grants from the NSF and Mathers Foundation.
From Brownian motion to power of fluctuations
Directory of Open Access Journals (Sweden)
B. Berche
2012-12-01
Full Text Available The year 2012 marks the 140th birth anniversary of Marian Smoluchowski (28.05.1872-5.09.1917, a man who "made ground-breaking contribution to the theory of Brownian motion, the theory of sedimentation, the statistical nature of the Second Law, the theory and practice of density fluctuations (critical opalescence. During his final years of scientific creativity his pioneering theory of coagulation and diffusion-limited reaction rate appeared. These outstanding achievements present true gems which dominate the description of soft matter physics and chemical physics as well as the related areas up till now!" This quotation was taken from the lecture by Peter Hanggi given at international conference Statistical Physics: Modern Trends and Applications that took place in Lviv, Ukraine on July 3-6, 2012 (see conference web-page for more details and was dedicated to the commemoration of Smoluchowski's work. This and forthcoming issues of the Condensed Matter Physics contain papers presented at this conference.
Spherical particle Brownian motion in viscous medium as non-Markovian random process
International Nuclear Information System (INIS)
Morozov, Andrey N.; Skripkin, Alexey V.
2011-01-01
The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered. -- Highlights: → Description of Brownian motion considering the entrainment of medium is developed. → We find the equations for statistical characteristics of impulse fluctuations. → Brownian motion at small time intervals is considered. → Theoretical results and experimental data are compared.
Indian Academy of Sciences (India)
IMTECH),. Chandigarh. Praveen Kumar is pursuing his PhD in chemical dynamics at. Panjab University,. Chandigarh. Keywords. Chemical oscillations, autoca-. talYSis, Lotka-Volterra model, bistability, hysteresis, Briggs-. Rauscher reaction.
Indian Academy of Sciences (India)
the law of mass-action that every simple reaction approaches ... from thermodynamic equilibrium. Such oscillating systems cor- respond to thermodynamically open systems. .... experimentally observable, and the third is always unstable.
Mezzasalma, Stefano A
2007-03-15
The theoretical basis of a recent theory of Brownian relativity for polymer solutions is deepened and reexamined. After the problem of relative diffusion in polymer solutions is addressed, its two postulates are formulated in all generality. The former builds a statistical equivalence between (uncorrelated) timelike and shapelike reference frames, that is, among dynamical trajectories of liquid molecules and static configurations of polymer chains. The latter defines the "diffusive horizon" as the invariant quantity to work with in the special version of the theory. Particularly, the concept of universality in polymer physics corresponds in Brownian relativity to that of covariance in the Einstein formulation. Here, a "universal" law consists of a privileged observation, performed from the laboratory rest frame and agreeing with any diffusive reference system. From the joint lack of covariance and simultaneity implied by the Brownian Lorentz-Poincaré transforms, a relative uncertainty arises, in a certain analogy with quantum mechanics. It is driven by the difference between local diffusion coefficients in the liquid solution. The same transformation class can be used to infer Fick's second law of diffusion, playing here the role of a gauge invariance preserving covariance of the spacetime increments. An overall, noteworthy conclusion emerging from this view concerns the statistics of (i) static macromolecular configurations and (ii) the motion of liquid molecules, which would be much more related than expected.
Nonlinear (Anharmonic Casimir Oscillator
Directory of Open Access Journals (Sweden)
Habibollah Razmi
2011-01-01
Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.
Discrete repulsive oscillator wavefunctions
International Nuclear Information System (INIS)
Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo
2009-01-01
For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.
On entanglement in neutrino mixing and oscillations
International Nuclear Information System (INIS)
Blasone, Massimo; Dell'Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio
2010-01-01
We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.
On entanglement in neutrino mixing and oscillations
Energy Technology Data Exchange (ETDEWEB)
Blasone, Massimo; Dell' Anno, Fabio; De Siena, Silvio; Illuminati, Fabrizio, E-mail: blasone@sa.infn.i [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (Italy)
2010-06-01
We report on recent results about entanglement in the context of particle mixing and oscillations. We study in detail single-particle entanglement arising in two-flavor neutrino mixing. The analysis is performed first in the context of Quantum Mechanics, and then for the case of Quantum Field Theory.
Topological phase in two flavor neutrino oscillations
International Nuclear Information System (INIS)
Mehta, Poonam
2009-01-01
We show that the phase appearing in neutrino flavor oscillation formulae has a geometric and topological contribution. We identify a topological phase appearing in the two flavor neutrino oscillation formula using Pancharatnam's prescription of quantum collapses between nonorthogonal states. Such quantum collapses appear naturally in the expression for appearance and survival probabilities of neutrinos. Our analysis applies to neutrinos propagating in vacuum or through matter. For the minimal case of two flavors with CP conservation, our study shows for the first time that there is a geometric interpretation of the neutrino oscillation formulae for the detection probability of neutrino species.
Energy Technology Data Exchange (ETDEWEB)
Viennot, David, E-mail: david.viennot@utinam.cnrs.fr; Aubourg, Lucile
2016-02-15
We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another part presents a disordered dynamics. For the quantum analogue, the chimera behaviour deals with the entanglement between the spins of the chain. We discuss the entanglement properties, quantum chaos, quantum disorder and semi-classical similarity of our quantum chimera system. The quantum chimera concept is novel and induces new perspectives concerning the entanglement of multipartite systems. - Highlights: • We propose a spin chain model with long range couplings having purely quantum states similar to the classical chimera states. • The quantum chimera states are characterized by the coexistence of strongly entangled and non-entangled spins in the same chain. • The quantum chimera states present some characteristics of quantum chaos.
International Nuclear Information System (INIS)
Viennot, David; Aubourg, Lucile
2016-01-01
We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another part presents a disordered dynamics. For the quantum analogue, the chimera behaviour deals with the entanglement between the spins of the chain. We discuss the entanglement properties, quantum chaos, quantum disorder and semi-classical similarity of our quantum chimera system. The quantum chimera concept is novel and induces new perspectives concerning the entanglement of multipartite systems. - Highlights: • We propose a spin chain model with long range couplings having purely quantum states similar to the classical chimera states. • The quantum chimera states are characterized by the coexistence of strongly entangled and non-entangled spins in the same chain. • The quantum chimera states present some characteristics of quantum chaos.
Browndye: A software package for Brownian dynamics
Huber, Gary A.; McCammon, J. Andrew
2010-11-01
A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems. Program summaryProgram title: Browndye Catalogue identifier: AEGT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license, included in distribution No. of lines in distributed program, including test data, etc.: 143 618 No. of bytes in distributed program, including test data, etc.: 1 067 861 Distribution format: tar.gz Programming language: C++, OCaml ( http://caml.inria.fr/) Computer: PC, Workstation, Cluster Operating system: Linux Has the code been vectorised or parallelized?: Yes. Runs on multiple processors with shared memory using pthreads RAM: Depends linearly on size of physical system Classification: 3 External routines: uses the output of APBS [1] ( http://www.poissonboltzmann.org/apbs/) as input. APBS must be obtained and installed separately. Expat 2.0.1, CLAPACK, ocaml-expat, Mersenne Twister. These are included in the Browndye distribution. Nature of problem: Exploration and determination of rate constants of bimolecular interactions involving large biological molecules. Solution method: Brownian dynamics with electrostatic, excluded volume, van der Waals, and desolvation forces. Running time: Depends linearly on size of physical system and quadratically on precision of results. The included example executes in a few minutes.
Engineering Autonomous Chemomechanical Nanomachines Using Brownian Ratchets
Lavella, Gabriel
Nanoscale machines which directly convert chemical energy into mechanical work are ubiquitous in nature and are employed to perform a diverse set of tasks such as transporting molecules, maintaining molecular gradients, and providing motion to organisms. Their widespread use in nature suggests that large technological rewards can be obtained by designing synthetic machines that use similar mechanisms. This thesis addresses the technological adaptation of a specific mechanism known as the Brownian ratchet for the design of synthetic autonomous nanomachines. My efforts were focused more specifically on synthetic chemomechanical ratchets which I deem will be broadly applicable in the life sciences. In my work I have theoretically explored the biophysical mechanisms and energy landscapes that give rise to the ratcheting phenomena and devised devices that operate off these principles. I demonstrate two generations of devices that produce mechanical force/deformation in response to a user specified ligand. The first generation devices, fabricatied using a combination nanoscale lithographic processes and bioconjugation techniques, were used to provide evidence that the proposed ratcheting phenomena can be exploited in synthetic architectures. Second generation devices fabricated using self-assembled DNA/hapten motifs were constructed to gain a precise understanding of ratcheting dynamics and design constraints. In addition, the self-assembled devices enabled fabrication en masse, which I feel will alleviate future experimental hurdles in analysis and facilitate its adaptation to technologies. The product of these efforts is an architecture that has the potential to enable numerous technologies in biosensing and drug delivery. For example, the coupling of molecule-specific actuation to the release of drugs or signaling molecules from nanocapsules or porous materials could be transformative. Such architectures could provide possible avenues to pressing issues in biology and
Energy Technology Data Exchange (ETDEWEB)
Chandra, J; Scott, A C
1983-01-01
Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.
How superdiffusion gets arrested: Ecological encounters explain shift from Lévy to Brownian movement
De Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Van de Koppel, J.
2014-01-01
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when
How superdiffusion gets arrested: ecological encounters explain shift from Levy to Brownian movement
de Jager, M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; de Koppel, J.
2014-01-01
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when
How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement
Jager, de M.; Bartumeus, F.; Kölzsch, A.; Weissing, F.J.; Hengeveld, G.M.; Nolet, B.A.; Herman, P.M.J.; Koppel, van de J.
2014-01-01
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when
Exponential functionals of Brownian motion, I: Probability laws at fixed time
Matsumoto, Hiroyuki; Yor, Marc
2005-01-01
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
de Jager, Monique; Bartumeus, Frederic; Kolzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M. J.; de Koppel, Johan van
2014-01-01
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when
de Jager, Monique; Bartumeus, Frederic; Kölzsch, Andrea; Weissing, Franz J.; Hengeveld, Geerten M.; Nolet, Bart A.; Herman, Peter M.J.; van de Koppel, Johan
2014-01-01
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when
On modeling animal movements using Brownian motion with measurement error.
Pozdnyakov, Vladimir; Meyer, Thomas; Wang, Yu-Bo; Yan, Jun
2014-02-01
Modeling animal movements with Brownian motion (or more generally by a Gaussian process) has a long tradition in ecological studies. The recent Brownian bridge movement model (BBMM), which incorporates measurement errors, has been quickly adopted by ecologists because of its simplicity and tractability. We discuss some nontrivial properties of the discrete-time stochastic process that results from observing a Brownian motion with added normal noise at discrete times. In particular, we demonstrate that the observed sequence of random variables is not Markov. Consequently the expected occupation time between two successively observed locations does not depend on just those two observations; the whole path must be taken into account. Nonetheless, the exact likelihood function of the observed time series remains tractable; it requires only sparse matrix computations. The likelihood-based estimation procedure is described in detail and compared to the BBMM estimation.
Brownian dynamic simulations and experiments of MR fluids
International Nuclear Information System (INIS)
Segovia-Gutiérrez, J P; Vicente, J de; Hidalgo, R; Puertas, A M
2013-01-01
The use of computational techniques in magnetorheology is not new. I general, these approaches assume dipolar magnetic interactions, hard sphere repulsions, and no-slip conditions. In this contribution we focus on the dynamics of the equilibrium state in the presence of uniaxial DC fields. To achieve this goal we make use of Brownian Dynamic Simulations. We highlight the importance of the Brownian forces versus magnetic dipolar interaction in the range of low magnetic field strengths. We monitor the formation of columnar structures and their dynamics, in competition with the Brownian motion, until a hexatic crystal phase appears at high field strengths for monodisperse systems. The shear viscosity is computed from the Einstein relation and eventually compared with experimental data at very low-shear rates. A reasonably good agreement between both data sets is observed.
Nonparametric Regression with Subfractional Brownian Motion via Malliavin Calculus
Directory of Open Access Journals (Sweden)
Yuquan Cang
2014-01-01
Full Text Available We study the asymptotic behavior of the sequence Sn=∑i=0n-1K(nαSiH1(Si+1H2-SiH2, as n tends to infinity, where SH1 and SH2 are two independent subfractional Brownian motions with indices H1 and H2, respectively. K is a kernel function and the bandwidth parameter α satisfies some hypotheses in terms of H1 and H2. Its limiting distribution is a mixed normal law involving the local time of the sub-fractional Brownian motion SH1. We mainly use the techniques of Malliavin calculus with respect to sub-fractional Brownian motion.
Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion
Directory of Open Access Journals (Sweden)
Kaminsky A. V.
2010-04-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the amplitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes ("fluctuation amplitudes" of the spectra of stochastic processes upon rotation of the Earth.
Cosmophysical Factors in the Fluctuation Amplitude Spectrum of Brownian Motion
Directory of Open Access Journals (Sweden)
Kaminsky A. V.
2010-07-01
Full Text Available Phenomenon of the regular variability of the fine structure of the fluctuation in the am- plitude distributions (shapes of related histograms for the case of Brownian motion was investigated. We took an advantage of the dynamic light scattering method (DLS to get a stochastically fluctuated signal determined by Brownian motion. Shape of the histograms is most likely to vary, synchronous, in two proximally located independent cells containing Brownian particles. The synchronism persists in the cells distant at 2 m from each other, and positioned meridionally. With a parallel-wise positioning of the cells, high probability of the synchronous variation in the shape of the histograms by local time has been observed. This result meets the previous conclusion about the dependency of histogram shapes (“fluctuation amplitudes” of the spectra of stochastic processes upon rotation of the Earth.
Non-colliding Brownian Motions and the Extended Tacnode Process
Johansson, Kurt
2013-04-01
We consider non-colliding Brownian motions with two starting points and two endpoints. The points are chosen so that the two groups of Brownian motions just touch each other, a situation that is referred to as a tacnode. The extended kernel for the determinantal point process at the tacnode point is computed using new methods and given in a different form from that obtained for a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the extended kernel is also different from that obtained for the extended tacnode kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the correlation kernel for a finite number of non-colliding Brownian motions starting at two points and ending at arbitrary points.
Stochastic calculus for fractional Brownian motion and related processes
Mishura, Yuliya S
2008-01-01
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0
Brownian gas models for extreme-value laws
International Nuclear Information System (INIS)
Eliazar, Iddo
2013-01-01
In this paper we establish one-dimensional Brownian gas models for the extreme-value laws of Gumbel, Weibull, and Fréchet. A gas model is a countable collection of independent particles governed by common diffusion dynamics. The extreme-value laws are the universal probability distributions governing the affine scaling limits of the maxima and minima of ensembles of independent and identically distributed one-dimensional random variables. Using the recently introduced concept of stationary Poissonian intensities, we construct two gas models whose global statistical structures are stationary, and yield the extreme-value laws: a linear Brownian motion gas model for the Gumbel law, and a geometric Brownian motion gas model for the Weibull and Fréchet laws. The stochastic dynamics of these gas models are studied in detail, and closed-form analytical descriptions of their temporal correlation structures, their topological phase transitions, and their intrinsic first-passage-time fluxes are presented. (paper)
Deterministic Brownian motion generated from differential delay equations.
Lei, Jinzhi; Mackey, Michael C
2011-10-01
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of chaotic solutions of the same equation. Our results show that solutions of the deterministic equation with randomly selected initial conditions display a Gaussian-like density for long time, but the densities are supported on an interval of finite measure. Using these chaotic solutions as velocities, we are able to produce Brownian-like motions, which show statistical properties akin to those of a classical Brownian motion over both short and long time scales. Several conjectures are formulated for the probabilistic properties of the solution of the differential delay equation. Numerical studies suggest that these conjectures could be "universal" for similar types of "chaotic" dynamics, but we have been unable to prove this.
Algorithm for generating a Brownian motion on a sphere
International Nuclear Information System (INIS)
Carlsson, Tobias; Elvingson, Christer; Ekholm, Tobias
2010-01-01
We present a new algorithm for generation of a random walk on a two-dimensional sphere. The algorithm is obtained by viewing the 2-sphere as the equator in the 3-sphere surrounded by an infinitesimally thin band with boundary which reflects Brownian particles and then applying known effective methods for generating Brownian motion on the 3-sphere. To test the method, the diffusion coefficient was calculated in computer simulations using the new algorithm and, for comparison, also using a commonly used method in which the particle takes a Brownian step in the tangent plane to the 2-sphere and is then projected back to the spherical surface. The two methods are in good agreement for short time steps, while the method presented in this paper continues to give good results also for larger time steps, when the alternative method becomes unstable.
The Intersection Probability of Brownian Motion and SLEκ
Directory of Open Access Journals (Sweden)
Shizhong Zhou
2015-01-01
Full Text Available By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and SLEκ. Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal SLEκ and planar Brownian motion started from distinct points in an upper half-plane H-.
Stochastic flows in the Brownian web and net
Czech Academy of Sciences Publication Activity Database
Schertzer, E.; Sun, R.; Swart, Jan M.
2014-01-01
Roč. 227, č. 1065 (2014), s. 1-160 ISSN 0065-9266 R&D Projects: GA ČR GA201/07/0237; GA ČR GA201/09/1931 Institutional support: RVO:67985556 Keywords : Brownian web * Brownian net * stochastic flow of kernels * measure-valued process * Howitt-Warren flow * linear system * random walk in random environment * finite graph representation Subject RIV: BA - General Mathematics Impact factor: 1.727, year: 2014 http://library.utia.cas.cz/separaty/2013/SI/swart-0396636.pdf
On the Generalized Brownian Motion and its Applications in Finance
DEFF Research Database (Denmark)
Høg, Esben; Frederiksen, Per; Schiemert, Daniel
This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force...... of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable...
Survival probabilities for branching Brownian motion with absorption
Harris, John; Harris, Simon
2007-01-01
We study a branching Brownian motion (BBM) with absorption, in which particles move as Brownian motions with drift $-\\rho$, undergo dyadic branching at rate $\\beta>0$, and are killed on hitting the origin. In the case $\\rho>\\sqrt{2\\beta}$ the extinction time for this process, $\\zeta$, is known to be finite almost surely. The main result of this article is a large-time asymptotic formula for the survival probability $P^x(\\zeta>t)$ in the case $\\rho>\\sqrt{2\\beta}$, where $P^x$ is...
Finding viscosity of liquids from Brownian motion at students' laboratory
International Nuclear Information System (INIS)
Greczylo, Tomasz; Debowska, Ewa
2005-01-01
Brownian motion appears to be a good subject for investigation at advanced students' laboratory [1]. The paper presents such an investigation carried out in Physics Laboratory II at the Institute of Experimental Physics of Wroclaw University. The experiment has been designed to find viscosity of liquids from Brownian motion phenomenon. Authors use modern technology that helps to proceed with measurements and makes the procedure less time and effort consuming. Discussion of the process of setting up the experiment and the results obtained for three different solutions of glycerin in water are presented. Advantages and disadvantages of the apparatus are pointed out along with descriptions of possible future uses
Brownian motion of solitons in a Bose-Einstein condensate.
Aycock, Lauren M; Hurst, Hilary M; Efimkin, Dmitry K; Genkina, Dina; Lu, Hsin-I; Galitski, Victor M; Spielman, I B
2017-03-07
We observed and controlled the Brownian motion of solitons. We launched solitonic excitations in highly elongated [Formula: see text] Bose-Einstein condensates (BECs) and showed that a dilute background of impurity atoms in a different internal state dramatically affects the soliton. With no impurities and in one dimension (1D), these solitons would have an infinite lifetime, a consequence of integrability. In our experiment, the added impurities scatter off the much larger soliton, contributing to its Brownian motion and decreasing its lifetime. We describe the soliton's diffusive behavior using a quasi-1D scattering theory of impurity atoms interacting with a soliton, giving diffusion coefficients consistent with experiment.
Coherent states in quantum mechanics
International Nuclear Information System (INIS)
Rodrigues, R. de Lima; Fernandes Junior, Damasio; Batista, Sheyla Marques
2001-12-01
We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out. (author)
Coherent states in quantum mechanics
Rodrigues, R D L; Fernandes, D
2001-01-01
We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Two point function for a simple general relativistic quantum model
Colosi, Daniele
2007-01-01
We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.
Rae, Alastair I M
2007-01-01
PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC
Phase synchronization for two Brownian motors with bistable coupling on a ratchet
International Nuclear Information System (INIS)
Mateos, Jose L.; Alatriste, F.R.
2010-01-01
Graphical abstract: We study phase synchronization for a walker with two Brownian motors with bistable coupling on a ratchet and show a connection between synchronization and optimal transport. - Abstract: We study phase synchronization for a walker on a ratchet potential. The walker consist of two particles coupled by a bistable potential that allow the interchange of the order of the particles while moving through a one-dimensional asymmetric periodic ratchet potential. We consider the deterministic and the stochastic dynamics of the center of mass of the walker in a tilted ratchet potential with an external periodic forcing, in the overdamped case. The ratchet potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the absence of external periodic forcing. This oscillator has an intrinsic frequency that can be entrained with the frequency of the external driving. We introduced a linear phase through a set of discrete time events and the associated average frequency, and show that this frequency can be synchronized with the frequency of the external driving. In this way, we can properly characterize the phenomenon of synchronization through Arnold tongues and show that the local maxima in the average velocity of the center of mass of the walker, both in the deterministic case and in the presence of noise, correspond to the borders of these Arnold tongues. In this way, we established a connection between optimal transport in ratchets and the phenomenon of phase synchronization.
Chester, Marvin
2003-01-01
Introductory text examines the classical quantum bead on a track: its state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; and bead in a spherical shell. Also, spin, matrices and structure of quantum mechanics; simplest atom; indistinguishable particles; and stationary-state perturbation theory.
Statistical properties of laser light scattering in Brownian medium
International Nuclear Information System (INIS)
Suwono; Santoso, Budi; Baiquni, A.
1983-01-01
Relationship between statistical properties of laser light scattering in Brownian medium and photon-counting distributions are described in detail. A coherence optical detection has been constructed and by using photon-counting technique the ensemble distribution of the scattered field within space and time coherence has been measured. Good agreement between theory and experiment is shown. (author)
Brownian Movement and Avogadro's Number: A Laboratory Experiment.
Kruglak, Haym
1988-01-01
Reports an experimental procedure for studying Einstein's theory of Brownian movement using commercially available latex microspheres and a video camera. Describes how students can monitor sphere motions and determine Avogadro's number. Uses a black and white video camera, microscope, and TV. (ML)
Occupation times distribution for Brownian motion on graphs
Desbois, J
2002-01-01
Considering a Brownian motion on a general graph, we study the joint law for the occupation times on all the bonds. In particular, we show that the Laplace transform of this distribution can be expressed as the ratio of two determinants. We give two formulations, with arc or vertex matrices, for this result and discuss a simple example. (letter to the editor)
Velocity persistence of Brownian particles generated in a glow discharge
International Nuclear Information System (INIS)
Hurd, A.J.; Ho, P.
1989-01-01
Quasielastic light scattering from Brownian particles in the rarefied environment of a glow discharge exhibits Gaussianlike intensity correlation functions owing to the long mean free paths of the particles. The shape of the correlation function depends on the particles' average thermal velocity and friction coefficient, which can be related to aggregate mass and structure, and indicates a crossover from kinetic to hydrodynamic behavior
Phase transition for absorbed Brownian motion with drift
International Nuclear Information System (INIS)
Ferrari, P.A.; Martinez, S.; San Martin, J.
1997-01-01
We study one-dimensional Brownian motion with constant drift toward the origin and initial distribution concentrated in the strictly positive real line. We say that at the first time the process hits the origin, it is absorbed. We study the asymptotic behavior, as t → ∞, of m t , the conditional distribution at time zero of the process conditioned on survival up to time t and on the process having a fixed value at time t. We find that there is a phase transition in the decay rate of the initial condition. For fast decay rate (subcritical case) m t is localized, in the critical case m t is located around √t, and for slow rates (supercritical case) m, is located around t. The critical rate is given by the decay of the minimal quasistationary distribution of this process. We also study in each case the asymptotic distribution of the process, scaled by √t, conditioned as before. We prove that in the subcritical case this distribution is a Brownian excursion. In the critical case it is a Brownian bridge attaining 0 for the first time at time 1, with some initial distribution. In the supercritical case, after centering around the expected value-which is of the order of t we show that this process converges to a Brownian bridge arriving at 0 at time 1 and with a Gaussian initial distribution
Brownian motion, Minkowski space and principle of special relativity
International Nuclear Information System (INIS)
Caubet, J.-P.
1977-01-01
From the assumption that the brownian diffusion locally behaves like an ideal gas (pressure being inversely proportional to volume according to Boyle's law) one can deduce the signature +++- of the Minkowski space, the Lorentz addition of velocities, and the principle of special relativity [fr
Entropy production of a Brownian ellipsoid in the overdamped limit.
Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik
2016-01-01
We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.