Anomalous Dissipative Quantum Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
CHEN Dian-Yong; BAI Zhan-Wu; DONG Yu-Bing
2008-01-01
We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as r-4and r-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case.
Quantum dynamics of the damped harmonic oscillator
Philbin, T G
2012-01-01
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the oscillator of interest. By using a continuum of oscillators as a reservoir, we canonically quantize the harmonic oscillator with Ohmic damping and also with general damping behaviour. The dynamics of a damped oscillator is determined by an arbitrary effective susceptibility that obeys Kramers-Kronig relations. This approach offers an alternative description of nano-mechanical oscillators and opto-mechanical systems.
Quantum control of harmonic oscillator networks
Genoni, Marco G; Kim, M S; Burgarth, Daniel
2011-01-01
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance spin systems, precise criterions to establish controllability, such as the so called rank criterion, are well known. However most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems -- encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nano-mechanical oscillators -- governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend t...
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
Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators
Institute of Scientific and Technical Information of China (English)
王雪红; 郭军义; 李艳
2012-01-01
In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ?/?λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.
Quantum Harmonic Oscillator Algebra and Link Invariants
Gómez, C
1991-01-01
The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang--Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander--Conway polynomial. The $R$ matrix of $U_q (h_4)$ can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of $SU(2)_q$ at $q=e^{2 \\pi i/N}$ in the $N \\rightarrow \\infty$ limit.Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander--Conway polynomial.
Deformed quantum harmonic oscillator with diffusion and dissipation
Isar, A
2002-01-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.
Deformed quantum harmonic oscillator with diffusion and dissipation
Isar, A.; Scheid, W.
2002-07-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master equation and of equations of motion for observables depend on the deformation function. The steady-state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation.
Quantum kicked harmonic oscillator in contact with a heat bath
Prado Reynoso, M. Á.; López Vázquez, P. C.; Gorin, T.
2017-02-01
We consider the quantum harmonic oscillator in contact with a finite-temperature bath, modeled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between classical integrability and chaos, on the one hand, and ballistic or diffusive energy absorption, on the other. We then investigate the influence of the heat bath on the oscillator in each case. Phase-space techniques allow us to simulate the evolution of the system efficiently. In this way, we calculate high-resolution Wigner functions at long times, where the system approaches a quasistationary cyclic evolution. Thereby, we perform an accurate study of the thermodynamic properties of a nonintegrable, quantum chaotic system in contact with a heat bath at finite temperature. In particular, we find that the heat transfer between harmonic oscillator and heat bath is governed by Fourier's law.
Twisted Conformal Algebra and Quantum Statistics of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
J. Naji
2014-01-01
Full Text Available We consider noncommutative two-dimensional quantum harmonic oscillators and extend them to the case of twisted algebra. We obtained modified raising and lowering operators. Also we study statistical mechanics and thermodynamics and calculated partition function which yields the free energy of the system.
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Chou, Chia-Chun
2016-10-01
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.
Quantum Harmonic Oscillator State Control in a Squeezed Fock Basis
Kienzler, D.; Lo, H.-Y.; Negnevitsky, V.; Flühmann, C.; Marinelli, M.; Home, J. P.
2017-07-01
We demonstrate control of a trapped-ion quantum harmonic oscillator in a squeezed Fock state basis, using engineered Hamiltonians analogous to the Jaynes-Cummings and anti-Jaynes-Cummings forms. We demonstrate that for squeezed Fock states with low n the engineered Hamiltonians reproduce the √{n } scaling of the matrix elements which is typical of Jaynes-Cummings physics, and also examine deviations due to the finite wavelength of our control fields. Starting from a squeezed vacuum state, we apply sequences of alternating transfer pulses which allow us to climb the squeezed Fock state ladder, creating states up to excitations of n =6 with up to 8.7 dB of squeezing, as well as demonstrating superpositions of these states. These techniques offer access to new sets of states of the harmonic oscillator which may be applicable for precision metrology or quantum information science.
Unitary approach to the quantum forced harmonic oscillator
2014-01-01
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations are applied successively to Schr\\"odinger's equation reducing it to its simplest form. Therefore, instead of solving the original Schr\\"odinger's partial differential equation in time and space the problem is replaced by a system of ordinary differential eq...
Quantum optics. Quantum harmonic oscillator state synthesis by reservoir engineering.
Kienzler, D; Lo, H-Y; Keitch, B; de Clercq, L; Leupold, F; Lindenfelser, F; Marinelli, M; Negnevitsky, V; Home, J P
2015-01-02
The robust generation of quantum states in the presence of decoherence is a primary challenge for explorations of quantum mechanics at larger scales. Using the mechanical motion of a single trapped ion, we utilize reservoir engineering to generate squeezed, coherent, and displaced-squeezed states as steady states in the presence of noise. We verify the created state by generating two-state correlated spin-motion Rabi oscillations, resulting in high-contrast measurements. For both cooling and measurement, we use spin-oscillator couplings that provide transitions between oscillator states in an engineered Fock state basis. Our approach should facilitate studies of entanglement, quantum computation, and open-system quantum simulations in a wide range of physical systems. Copyright © 2015, American Association for the Advancement of Science.
Excitation with quantum light. I. Exciting a harmonic oscillator
Carreño, J. C. López; Laussy, F. P.
2016-12-01
We present a two-part study of the excitation of an optical target by quantum light. In this first part, we introduce the problematic and address the first case of interest, that of exciting the quantum harmonic oscillator, corresponding to, e.g., a single-mode passive cavity or a noninteracting bosonic field. We introduce a mapping of the Hilbert space that allows to chart usefully the accessible regions. We then consider the quantum excitation from single-photon sources in the form of a two-level system under various regimes of (classical) pumping: incoherent, coherent, and in the Mollow triplet regime. We close this first part with an overview of the material to be covered in the subsequent work.
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.
Non-Markovian quantum Brownian motion of a harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Tang, J.
1994-02-01
We apply the density-matrix method to the study of quantum Brownian motion of a harmonic oscillator coupled to a heat bath, a system investigated previously by Caldeira and Leggett using a different method. Unlike the earlier work, in our derivation of the master equation the non-Markovian terms are maintained. Although the same model of interaction is used, discrepancy is found between their results and our equation in the Markovian limit. We also point out that the particular interaction model used by both works cannot lead to the phenomenological generalized Langevin theory of Kubo.
On quantum harmonic oscillator being subjected to absolute potential state
Indian Academy of Sciences (India)
SWAMI NITYAYOGANANDA
2017-01-01
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 frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as ‘like-potential’ energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remainsdormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity – this needs further research. The more the QOE, the greaterwill be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.
On quantum harmonic oscillator being subjected to absolute potential state
Nityayogananda, Swami
2017-01-01
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 frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very high dormant potential energy is referred to as `like-potential' energy in this paper. In the process a new wave function is generated. This new function, which corresponds to new sets of particles, has scope to raise the quantum oscillator energy (QOE) up to infinity. It is proposed to show that this high energy does not get cancelled but remains dormant. Further, it is proposed that the displacement about the equilibrium goes to zero when the vibration of the oscillator stops and then the QOE becomes infinity - this needs further research. The more the QOE, the greater will be the degree of dormancy. A simple mathematical model has been derived here to discuss the possibilities that are involved in the QHO under the above-mentioned boundary conditions.
Chou, C H; Yu, T; Chou, Chung-Hsien; Yu, Ting
2007-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment made up of many harmonic oscillators at arbitrary temperature for a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is known [Hu, Paz and Zhang, Phys. Rev. D \\textbf{45}, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolution operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We ...
Quantum Encoding and Entanglement in Terms of Phase Operators Associated with Harmonic Oscillator
Singh, Manu Pratap; Rajput, B. S.
2016-10-01
Realization of qudit quantum computation has been presented in terms of number operator and phase operators associated with one-dimensional harmonic oscillator and it has been demonstrated that the representations of generalized Pauli group, viewed in harmonic oscillator operators, allow the qudits to be explicitly encoded in such systems. The non-Hermitian quantum phase operators contained in decomposition of the annihilation and creation operators associated with harmonic oscillator have been analysed in terms of semi unitary transformations (SUT) and it has been shown that the non-vanishing analytic index for harmonic oscillator leads to an alternative class of quantum anomalies. Choosing unitary transformation and the Hermitian phase operator free from quantum anomalies, the truncated annihilation and creation operators have been obtained for harmonic oscillator and it has been demonstrated that any attempt of removal of quantum anomalies leads to absence of minimum uncertainty.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
DIÓGENES CAMPOS
2017-03-01
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 standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.
Covariant harmonic oscillators and coupled harmonic oscillators
Han, Daesoo; Kim, Young S.; Noz, Marilyn E.
1995-01-01
It is shown that the system of two coupled harmonic oscillators shares the basic symmetry properties with the covariant harmonic oscillator formalism which provides a concise description of the basic features of relativistic hadronic features observed in high-energy laboratories. It is shown also that the coupled oscillator system has the SL(4,r) symmetry in classical mechanics, while the present formulation of quantum mechanics can accommodate only the Sp(4,r) portion of the SL(4,r) symmetry. The possible role of the SL(4,r) symmetry in quantum mechanics is discussed.
Chou, Chung-Hsien; Yu, Ting; Hu, B L
2008-01-01
In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a single harmonic oscillator in a general environment plus a free harmonic oscillator. Since the exact one harmonic oscillator master equation is available [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)], the exact master equation with all its coefficients for this two harmonic oscillator model can be easily deduced from the known results of the single harmonic oscillator case. In the second part we give an influence functional treatment of this model and provide explicit expressions for the evolutionary operator of the reduced density matrix which are useful for the study of decoherence and disentanglement issues. We show three applications of this master equation: on the decoherence and disentanglement of two harmonic oscillators due to their interaction with a common environment under Markovian approximation, and a derivation of the uncertainty principle at finite temperature for a composite object, modeled by two interacting harmonic oscillators. The exact master equation for two, and its generalization to N, harmonic oscillators interacting with a general environment are expected to be useful for the analysis of quantum coherence, entanglement, fluctuations, and dissipation of mesoscopic objects toward the construction of a theoretical framework for macroscopic quantum phenomena.
The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
Schliemann, John
2013-01-01
It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.
Harmonic oscillator in Snyder space: The classical case and the quantum case
Indian Academy of Sciences (India)
Carlos Leiva
2010-02-01
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 harmonic oscillator is obtained through an effective mass and an effective frequency introduced in the model. This modified parameters give us a modified energy spectrum also.
On a Hidden Symmetry of Quantum Harmonic Oscillators
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We present a six parameter family of the square integrable wave functions for the linear harmonic oscillator, which cannot be obtained by the standard separation of variables. They are found by the action of corresponding maximal kinematical invariance group on the standard solutions. Some possible applications are briefly discussed.
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.
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1994-01-01
The symmetry algebra of the two-dimensional quantum harmonic oscillator with rational ratio of frequencies is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems.
Ground-state isolation and discrete flows in a rationally extended quantum harmonic oscillator
Cariñena, José F
2016-01-01
Ladder operators for the simplest version of a rationally extended quantum harmonic oscillator (REQHO) are constructed by applying a Darboux transformation to the quantum harmonic oscillator system. It is shown that the physical spectrum of the REQHO carries a direct sum of a trivial and an infinite-dimensional irreducible representation of the polynomially deformed bosonized osp(1|2) superalgebra. In correspondence with this the ground state of the system is isolated from other physical states but can be reached by ladder operators via non-physical energy eigenstates, which belong to either an infinite chain of similar eigenstates or to the chains with generalized Jordan states. We show that the discrete chains of the states generated by ladder operators and associated with physical energy levels include six basic generalized Jordan states, in comparison with the two basic Jordan states entering in analogous discrete chains for the quantum harmonic oscillator.
(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; XU Hao; YANG Jie-Chao; WANG Yu-Li; CHANG Di; LIN Yin; Helmut Kroger
2001-01-01
In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``
On the Bandgap quantum coupler and the harmonic oscillator interacting with a reservoir
Quijas, P C G
2007-01-01
In order to be able to study dissipation, the interaction between a single system and their environment was introduced in quantum mechanics. Master and quantum Langeving equations was derived and, also, decoherence was studied using this approach. One of the most used model in this field of research is a single harmonic oscillator interacting with an infinite number of harmonic oscillators. In this work we analytically solve, with the evolution operator method, the Schrodinger equation for this model in the case of resonance. Also we address a different aspect of the quantum computing with linear optics. That is, we propose the linear bandgap quantum coupler, in the cases N=2 and N=3, to generate a new phase operator $U_{dp}^{\\pi} $ working on the two and three qubits basis like an alternative realization of a quantum phase gate.
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.
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
On The Harmonic Oscillator Group
Lopez, Raquel M; Vega-Guzman, Jose M
2011-01-01
We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Andrews, David L.; Romero, Luciana C. Davila
2009-01-01
The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…
Evolution of a quantum harmonic oscillator coupled to a minimal thermal environment
Vidiella-Barranco, A.
2016-10-01
In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B), initially in a thermal state. Two types of interaction Hamiltonians are considered, and the time-evolution of the reduced density operator of oscillator A is compared to the one obtained from the usual master equation approach, i.e., assuming that oscillator A is coupled to a large reservoir. An analysis of the linear entropy evolution of oscillator A shows that simplified models may be able to describe important features related to the phenomenon of decoherence, such as the rapid growth of the linear entropy, as well as its dependence on the effective temperature of the environment.
Directory of Open Access Journals (Sweden)
Xiaowei Liu, Lingen Chen, Feng Wu, Fengrui Sun
2015-01-01
Full Text Available The optimal performance of an irreversible quantum Carnot refrigerator with working medium consisting of many non-interacting harmonic oscillators is investigated in this paper. The quantum refrigerator cycle is composed of two isothermal processes and two irreversible adiabatic processes, and the irreversibilities of heat resistance, internal friction and bypass heat leakage are considered. By using the quantum master equation, semi-group approach and finite time thermodynamics (FTT, this paper derives the cooling load and coefficient of performance (COP of the quantum refrigeration cycle and provides detailed numerical examples. At high temperature limit, the cooling load versus COP characteristic curves are plotted, and effects of internal friction and bypass heat leakage on the optimal performance of the quantum refrigerator are discussed. Three special cases, i.e., endoreversible, frictionless and without bypass heat leakage, are discussed in brief.
Saha, Anirban
2015-01-01
We investigate the quantum mechanical transitions, induced by the combined effect of Gravitational wave (GW) and noncommutative (NC) structure of space, among the states of a 2-dimensional harmonic oscillator. The phonon modes excited by the passing GW within the resonant bar-detector are formally identical to forced harmonic oscillator and they represent a length variation of roughly the same order of magnitude as the characteristic length-scale of spatial noncommutativity estimated from the phenomenological upper bound of the NC parameter. This motivates our present work. We employ a number of different GW wave-forms that are typically expected from possible astronomical sources. We find that the transition probablities are quite sensitive to the nature of polarization of the GW. We further elaborate on the particular type of sources of GW radiation which can induce transitions that can be used as effective probe of the spatial noncommutative structure.
Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator's Wave Functions
Institute of Scientific and Technical Information of China (English)
LU Hai-Liang; FAN Hong-Yi
2007-01-01
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator's wave functions.The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S(r)Hm,n(μa1+, μa2+)|00〉, which is the minimum uncertainty state for sum squeezing, in 〈η| representation is calculated.
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.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; 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 ...
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
Directory of Open Access Journals (Sweden)
Lock Yue Chew
2014-04-01
Full Text Available In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state.
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.
Relativistic Harmonic Oscillators and Hadronic Structures in the Quantum-Mechanics Curriculum
Kim, Y. S.; Noz, Marilyn E.
1978-01-01
A relativistic harmonic-oscillator formalism which is mathematically simple as the nonrelativistic harmonic oscillator is given. In view of its effectiveness in describing Lorentz-deformed hadrons, the inclusion of this formalism in a first-year graduate course will make the results of high-energy experiments more understandable. (BB)
Wang, Zhiguo; Liang, Zhenguo
2017-04-01
In this paper we prove an infinite dimensional KAM theorem, in which the assumptions on the derivatives of the perturbation in [24] are weakened from polynomial decay to logarithmic decay. As a consequence, we can apply it to 1D quantum harmonic oscillators and prove the reducibility of the linear harmonic oscillator, T=-\\frac{{{\\text{d}}2}}{\\text{d}{{x}2}}+{{x}2} , on {{L}2}≤ft({R}\\right) perturbed by the quasi-periodic in the time potential V(x,ω t;ω ) with logarithmic decay. This proves the pure-point nature of the spectrum of the Floquet operator K, where K:=‑i∑k=1nωk∂∂θk‑d2dx2+x2+εV(x,θω) is defined on {{L}2}≤ft({R}\\right)\\otimes {{L}2}≤ft({{{T}}n}\\right) , and the potential V(x,θ ;ω ) has logarithmic decay as well as its gradient in ω.
MAVRI, J; BERENDSEN, HJC
1994-01-01
A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the unperturbe
MAVRI, J; BERENDSEN, HJC
1994-01-01
A density-matrix evolution method [Berendsen and Mavri, J. Phys. Chem. 97, 13464 (1993)] coupled to a classical molecular dynamics simulation was applied to study a quantum harmonic oscillator immersed in a bath of Lennard-Jones particles. Eigenfunctions of the three, lowest levels of the unperturbe
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Thermodynamical analysis of a quantum heat engine based on harmonic oscillators
Insinga, Andrea; Andresen, Bjarne; Salamon, Peter
2016-07-01
Many models of heat engines have been studied with the tools of finite-time thermodynamics and an ensemble of independent quantum systems as the working fluid. Because of their convenient analytical properties, harmonic oscillators are the most frequently used example of a quantum system. We analyze different thermodynamical aspects with the final aim of the optimization of the performance of the engine in terms of the mechanical power provided during a finite-time Otto cycle. The heat exchange mechanism between the working fluid and the thermal reservoirs is provided by the Lindblad formalism. We describe an analytical method to find the limit cycle and give conditions for a stable limit cycle to exist. We explore the power production landscape as the duration of the four branches of the cycle are varied for short times, intermediate times, and special frictionless times. For short times we find a periodic structure with atolls of purely dissipative operation surrounding islands of divergent behavior where, rather than tending to a limit cycle, the working fluid accumulates more and more energy. For frictionless times the periodic structure is gone and we come very close to the global optimal operation. The global optimum is found and interestingly comes with a particular value of the cycle time.
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.
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
Time dependent quantum harmonic oscillator subject to a sudden change of mass: continuous solution
Energy Technology Data Exchange (ETDEWEB)
Moya C, H. [INAOE, Coordinacion de Optica, AP 51 y 216, 72000 Puebla (Mexico); Fernandez G, M. [Depto. de Fisica, CBI, Universidad Autonoma Metropolitana - Iztapalapa, 09340, Mexico, D.F. AP 55-534 (Mexico)
2007-07-01
We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a sub period function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism requires an ad hoc transformation of the original differential equation and is also applicable for rapid, although not necessarily instantaneous, mass variations. (Author)
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M
2001-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, Miguel
2001-07-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
Lorente, M.
2004-01-01
The Kravchuk and Meixner polynomials of discrete variable are introduced for the discrete models of the harmonic oscillator and hydrogen atom. Starting from Rodrigues formula we construct raising and lowering operators, commutation and anticommutation relations. The physical properties of discrete models are figured out through the equivalence with the continuous models obtained by limit process.
Nonclassical phase-space trajectories for the damped harmonic quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Pachon, L.A. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); CeiBA - Complejidad, Bogota D.C. (Colombia); Ingold, G.-L., E-mail: gert.ingold@physik.uni-augsburg.de [Institut fuer Physik, Universitaet Augsburg, Universitaetsstrasse 1, D-86135 Augsburg (Germany); Dittrich, T. [Departamento de Fisica, Universidad Nacional de Colombia, Bogota D.C. (Colombia); CeiBA - Complejidad, Bogota D.C. (Colombia)
2010-10-05
Graphical abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation and the appearance of nonclassical trajectories is discussed. - Abstract: The phase-space path-integral approach to the damped harmonic oscillator is analyzed beyond the Markovian approximation. It is found that pairs of nonclassical trajectories contribute to the path-integral representation of the Wigner propagating function. Due to the linearity of the problem, the sum coordinate of a pair still satisfies the classical equation of motion. Furthermore, it is shown that the broadening of the Wigner propagating function of the damped oscillator arises due to the time-nonlocal interaction mediated by the heat bath.
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
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.
Decoherence in a quantum harmonic oscillator monitored by a Bose-Einstein condensate
Brouard, S; Sokolovski, D
2010-01-01
We investigate the dynamics of a quantum oscillator, whose evolution is monitored by a Bose-Einstein condensate (BEC) trapped in a symmetric double well potential. It is demonstrated that the oscillator may experience various degrees of decoherence depending on the variable being measured and the state in which the BEC is prepared. These range from a `coherent' regime in which only the variances of the oscillator position and momentum are affected by measurement, to a slow (power law) or rapid (Gaussian) decoherence of the mean values themselves.
Mandal, Swapan
2017-03-01
The classical harmonic oscillator with time dependent mass and frequency is investigated to obtain a closed form exact analytical solution. It is found that the closed form analytical solutions are indeed possible if the time dependent mass of the oscillator is inversely proportional to the time dependent frequency. The scaled wronskian obtained from the linearly independent solutions of the equation of motion of the classical oscillator is used to obtain the solution corresponding to its quantum mechanical counterpart. The analytical solution of the present oscillator is used to obtain the squeezing effects of the input coherent light. In addition to the possibilities of getting the squeezed states, the present solution will be of use for investigating various quantum statistical properties of the radiation fields. As an example, we investigate the antibunching of the input thermal (chaotic) light coupled to the oscillator. Therefore, the appearance of the photon antibunching does not warrant the squeezing and vice-versa. The exact solution is obtained at the cost of the stringent condition where the product of time dependent mass and frequency of the oscillator is time invariant.
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.
A model of the two-dimensional quantum harmonic oscillator in an $AdS_3$ background
Frick, Rudolf
2016-01-01
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\\"odinger picture in which the analogs of the Schr\\"odinger 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 $AdS_3$ spacetime. In this picture, we have a metamorphosis of the Heisenberg's uncertainty relations.
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.)
The q-DEFORMED SCHRÖDINGER Equation of the Harmonic Oscillator on the Quantum Euclidean Space
Carow-Watamura, Ursula; Watamura, Satoshi
We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.
A quantum quasi-harmonic nonlinear oscillator with an isotonic term
Energy Technology Data Exchange (ETDEWEB)
Rañada, Manuel F., E-mail: mfran@unizar.es [Dep. de Física Teórica and IUMA, Universidad de Zaragoza, 50009 Zaragoza (Spain)
2014-08-01
The properties of a nonlinear oscillator with an additional term k{sub g}/x², characterizing the isotonic oscillator, are studied. The nonlinearity affects to both the kinetic term and the potential and combines two nonlinearities associated to two parameters, κ and k{sub g}, in such a way that for κ = 0 all the characteristics of the standard isotonic system are recovered. The first part is devoted to the classical system and the second part to the quantum system. This is a problem of quantization of a system with position-dependent mass of the form m(x) = 1/(1 − κx²), with a κ-dependent non-polynomial rational potential and with an additional isotonic term. The Schrödinger equation is exactly solved and the (κ, k{sub g})-dependent wave functions and bound state energies are explicitly obtained for both κ < 0 and κ > 0.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
MAVRI, J; LENSINK, M; BERENDSEN, HJC
1994-01-01
A density matrix evolution (DME) method (Berendsen, H. J. C., and Mavri, J., 1993, J. phys. Chem., 97, 13464) to simulate the dynamics of quantum systems embedded in a classical environment is applied to study the inelastic collisions of a classical particle with a five level quantum harmonic
Harmonic oscillator model for the helium atom
Carlsen, Martin
2015-01-01
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not based on the choice of correct trial wave function. Three harmonic oscillators and thus three quantum numbers are sufficient to describe the two-electron system. We derive a simple formula for the energy in the general case and in the special case of the Wannier Ridge. For a set of quantum numbers the distance to the electrons and the angle between the electrons are uniquely determined as the intersection between three surfaces. We show that the excited states converge either towards ionization thresholds or towards extreme parallel or antiparallel states and provide an estimate of the ground state energy.
Nonlinear harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' (Italy); Inozemtsev, V I [Joint Institute for Nuclear Research, Dubna (Russian Federation)
2002-12-06
The existence is noted of assemblies of an arbitrary number of complex oscillators, or equivalently, of an arbitrary even number of real oscillators, characterized by Newtonian equations of motion ('acceleration equal force') with one-body velocity-dependent linear forces and many-body velocity-independent cubic forces, all the nonsingular solutions of which are isochronous (completely periodic with the same period). As for the singular solutions, as usual they emerge, in the context of the initial-value problem, from a closed domain in phase space having lower dimensionality.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.
Performance of a quantum heat engine cycle working with harmonic oscillator systems
Institute of Scientific and Technical Information of China (English)
WANG JianHui; HE JiZhou; MAO ZhiYuan
2007-01-01
A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are discussed in brief.
Harmonic oscillator: an analysis via Fourier series
de Castro, A S
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
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.
Bonatsos, Dennis; Kolokotronis, P; Lenis, D; Bonatsos, Dennis
1994-01-01
The symmetry algebra of the two-dimensional anisotropic quantum harmonic oscillator with rational ratio of frequencies, which is characterizing ``pancake'' nuclei, is identified as a non-linear extension of the u(2) algebra. The finite dimensional representation modules of this algebra are studied and the energy eigenvalues are determined using algebraic methods of general applicability to quantum superintegrable systems. For labelling the degenerate states an ``angular momentum'' operator is introduced, the eigenvalues of which are roots of appropriate generalized Hermite polynomials. In the special case with frequency ratio 2:1 the resulting algebra is identified as the finite W algebra W_3^{(2)}.
Harmonic oscillation in a spatially finite array waveguide.
Gordon, R
2004-12-01
A waveguide array is presented that behaves as an oscillator, showing periodic image reconstruction, focusing, and transverse wave-packet oscillation. The oscillator has a finite width, which removes the need for premature truncation. The array waveguide oscillator shows properties analogous to those of a pedagogically important one-dimensional quantum harmonic oscillator, which are fundamentally different from previously demonstrated oscillations in Wannier-Stark waveguide arrays. Calculations of the entire array waveguide oscillator are presented that quantify higher-order corrections to the coupled-mode approach. These results can be extended to waveguide oscillators in other systems, such as electrons in superlattices.
Harmonic Oscillators and Elementary Particles
Sobouti, Y
2016-01-01
Two dynamical systems with same symmetry should have features in common, and as far as their shared symmetry is concerned, one may represent the other. The three light quark constituents of the hadrons, a) have an approximate flavor SU(3) symmetry, b) have an exact color SU(3) symmetry, and c) as spin 1/2 particles, have a Lorentz SO(3,1) symmetry. So does a 3D harmonic oscillator. a) Its Hamiltonian has the SU(3) symmetry, breakable if the 3 fundamental modes of oscillation are not identical. b) The 3 directions of oscillation have the permutation symmetry. This enables one to create three copies of unbreakable SU(3) symmetry for each mode of the oscillation, and mimic the color of the elementary particles. And c) The Lagrangian of the 3D oscillator has the SO(3,1) symmetry. This can be employed to accommodate the spin of the particles. In this paper we draw up a one-to-one correspondence between the eigen modes of the Poisson bracket operator of the 3D oscillator and the flavor multiplets of the particles, ...
Marquette, Ian; Quesne, Christiane
2016-05-01
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent PIV, 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 Xm1,m2,…,mk 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.
Making space for harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Quantizing the damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Latimer, D C [Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235 (United States)
2005-03-04
We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that the unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.
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.
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)
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
Wigner Functions for harmonic oscillator in noncommutative phase space
Wang, Jianhua; Li, Kang; Dulat, Sayipjamal
2009-01-01
We study the Wigner Function in non-commutative quantum mechanics. By solving the time independent Schr\\"{o}dinger equation both on a non-commutative (NC) space and a non-commutative phase space, we obtain the Wigner Function for the harmonic oscillator on NC space and NC phase space respectively.
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Jeong-Ryeol Choi
2003-07-01
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. The uncertainty relation of the system is always larger than ħ=2 not only in number but also in the thermal state as expected. We used the diagonal elements of density operator satisfying Leouville–von Neumann equation to calculate various expectation values in the thermal state. We applied our theory to a special case which is the forced Caldirola–Kanai oscillator.
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.
The harmonic oscillator and nuclear physics
Rowe, D. J.
1993-01-01
The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.
Equity prices as a simple harmonic oscillator with noise
Ataullah, Ali; Tippett, Mark
2007-08-01
The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.
PT-symmetric quantum oscillator in an optical cavity
Longhi, Stefano
2016-01-01
The quantum harmonic oscillator with parity-time ($\\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and exactly-solvable model to investigate non-Hermitian extension of the Ehrenfest theorem. Here it is shown that transverse light dynamics in an optical resonator with off-axis longitudinal pumping can emulate a $\\mathcal{PT}$-symmetric quantum harmonic oscillator, providing an experimentally accessible system to investigate non-Hermitian coherent state propagation.
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Quantum entanglement of Pais-Uhlenbeck oscillators
Dimov, Hristo; Rashkov, Radoslav C; Vetsov, Tsvetan
2016-01-01
We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using the formalism of thermo-field dynamics. The entanglement entropy is computed for the specific cases of two and a ring of $N$ coupled Pais-Uhlenbeck oscillators of fourth order. It is shown that the entanglement entropy depends on the temperatures, frequencies and coupling parameters of the different degrees of freedom corresponding to harmonic oscillators. Finally, we advert to the information geometry theory by calculating the Fisher information metric for the considered system of coupled oscillators.
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
Sobolev Spaces Associated to the Harmonic Oscillator
Indian Academy of Sciences (India)
B Bongioanni; J L Torrea
2006-08-01
We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= - + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.
The Berry Phase for Simple Harmonic Oscillators
Suslov, Sergei K
2011-01-01
We evaluate the Berry phase for a "missing" family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables. It is obtained by the action of the maximal kinematical invariance group on the standard solutions. An explicit simple formula for the phase is found by integration with the help of a computer algebra system.
Harmonic Oscillators as Bridges between Theories: Einstein, Dirac, and Feynman
Kim, Y S; Noz, Marilyn E.
2004-01-01
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement, decoherence, and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of by two-by-two matrices commonly called $SL(2,c)$...
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even monomial perturbation, which we use to study the resulting...... U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...
Pisot q-coherent states quantization of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
quantum oscillator.
Ecological optimization of an irreversible harmonic oscillators Carnot heat engine
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
A model of an irreversible quantum Carnot heat engine with heat resistance,internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach,equations of some important performance parameters,such as power output,efficiency,exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
Ecolosical optimization of an irreversible harmonic oscillators Carnot heat engine
Institute of Scientific and Technical Information of China (English)
LIU XiaoWei; CHEN LinGen; WU Feng; SUN FengRui
2009-01-01
A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.
Sharma, Navneet; Rawat, Tarun Kumar; Parthasarathy, Harish; Gautam, Kumar
2016-06-01
The aim of this paper is to design a current source obtained as a representation of p information symbols \\{I_k\\} so that the electromagnetic (EM) field generated interacts with a quantum atomic system producing after a fixed duration T a unitary gate U( T) that is as close as possible to a given unitary gate U_g. The design procedure involves calculating the EM field produced by \\{I_k\\} and hence the perturbing Hamiltonian produced by \\{I_k\\} finally resulting in the evolution operator produced by \\{I_k\\} up to cubic order based on the Dyson series expansion. The gate error energy is thus obtained as a cubic polynomial in \\{I_k\\} which is minimized using gravitational search algorithm. The signal to noise ratio (SNR) in the designed gate is higher as compared to that using quadratic Dyson series expansion. The SNR is calculated as the ratio of the Frobenius norm square of the desired gate to that of the desired gate error.
Nonequilibrium quantum fluctuation relations for harmonic systems in nonthermal environments
Pagel, D.; Nalbach, P.; Alvermann, A.; Fehske, H.; Thorwart, M.
2013-10-01
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal) state. Starting from the exact solution for the oscillator dynamics we study fluctuations of the oscillator position as well as of the energy current through the oscillator under general nonequilibrium conditions. In particular, we formulate a fluctuation-dissipation relation for the oscillator position autocorrelation function that generalizes the standard result for the case of a single bath at thermal equilibrium. Moreover, we show that the generating function for the position operator fulfils a generalized Gallavotti-Cohen-like relation. For the energy transfer through the oscillator, we determine the average energy current together with the current fluctuations. Finally, we discuss the generalization of the cumulant generating function for the energy transfer to nonthermal bath preparations.
Physical realization of the Glauber quantum oscillator.
Gentilini, Silvia; Braidotti, Maria Chiara; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio
2015-11-02
More than thirty years ago Glauber suggested that the link between the reversible microscopic and the irreversible macroscopic world can be formulated in physical terms through an inverted harmonic oscillator describing quantum amplifiers. Further theoretical studies have shown that the paradigm for irreversibility is indeed the reversed harmonic oscillator. As outlined by Glauber, providing experimental evidence of these idealized physical systems could open the way to a variety of fundamental studies, for example to simulate irreversible quantum dynamics and explain the arrow of time. However, supporting experimental evidence of reversed quantized oscillators is lacking. We report the direct observation of exploding n = 0 and n = 2 discrete states and Γ0 and Γ2 quantized decay rates of a reversed harmonic oscillator generated by an optical photothermal nonlinearity. Our results give experimental validation to the main prediction of irreversible quantum mechanics, that is, the existence of states with quantized decay rates. Our results also provide a novel perspective to optical shock-waves, potentially useful for applications as lasers, optical amplifiers, white-light and X-ray generation.
Physical realization of the Glauber quantum oscillator
Gentilini, Silvia; Braidotti, Maria Chiara; Marcucci, Giulia; Delre, Eugenio; Conti, Claudio
2015-11-01
More than thirty years ago Glauber suggested that the link between the reversible microscopic and the irreversible macroscopic world can be formulated in physical terms through an inverted harmonic oscillator describing quantum amplifiers. Further theoretical studies have shown that the paradigm for irreversibility is indeed the reversed harmonic oscillator. As outlined by Glauber, providing experimental evidence of these idealized physical systems could open the way to a variety of fundamental studies, for example to simulate irreversible quantum dynamics and explain the arrow of time. However, supporting experimental evidence of reversed quantized oscillators is lacking. We report the direct observation of exploding n = 0 and n = 2 discrete states and Γ0 and Γ2 quantized decay rates of a reversed harmonic oscillator generated by an optical photothermal nonlinearity. Our results give experimental validation to the main prediction of irreversible quantum mechanics, that is, the existence of states with quantized decay rates. Our results also provide a novel perspective to optical shock-waves, potentially useful for applications as lasers, optical amplifiers, white-light and X-ray generation.
Braid group representations from a deformation of the harmonic oscillator algebra
Tarlini, Marco
2016-01-01
We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of representations of the algebra, that in the harmonic oscillator case are infinite dimensional, but on the subspace of the tensor product corresponding to the lowest weight vectors.
Entanglement dynamics for a conditionally kicked harmonic oscillator
Arrais, Eric G.; Sales, J. S.; de Almeida, N. G.
2016-08-01
The time evolution of the quantum kicked harmonic oscillator (KHO) is described by the Floquet operator which maps the state of the system immediately before one kick onto the state at a time immediately after the next. Quantum KHO is characterized by three parameters: the coupling strength V 0, the so-called Lamb-Dicke parameter η whose square is proportional to the effective Planck constant {{\\hslash }}{{eff}}, and the ratio T of the natural frequency of the oscillator and the kick frequency. To a given coupling strength and depending on T being a natural or irrational number, the phase space of the classical kicked oscillator can display different behaviors, as for example, stochastic webs or quasicrystal structures, thus showing a chaotic or localized behavior that is mirrored in the quantum phase space. On the other hand, the classical limit is studied letting {{\\hslash }}{{eff}} become negligible. In this paper we investigate how the ratio T, considered as integer, rational or irrational, influences the entanglement dynamics of the quantum KHO and study how the entanglement dynamics behaves when varying either V 0 or {{\\hslash }}{{eff}} parameters.
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
N D Hari Dass; Pradeep Ganesh
2002-08-01
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use of this perfect information cloning it would be possible to estimate the original state through measurements and make arbitrary number of copies of the estimator. We deﬁne the notion of a measurement ﬁdelity and calculate it for our case as well as for the Gaussian cloners.
Lipschitz spaces and bounded mean oscillation of harmonic mappings
Chen, Sh; Vuorinen, M; Wang, X
2012-01-01
In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to $BMO_{2}$ as a Banach space.
Effective harmonic oscillator description of anharmonic molecular vibrations
Indian Academy of Sciences (India)
Tapta Kanchan Roy; M Durga Prasad
2009-09-01
The validity of an effective harmonic oscillator approximation for anharmonic molecular vibrations is tested and compared with vibrational self consistent field and vibrational configurational interaction results. The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
The noncommutative harmonic oscillator in more than one dimensions
Hatzinikitas, A; Hatzinikitas, Agapitos; Smyrnakis, Ioannis
2002-01-01
The noncommutative harmonic oscillator in arbitrary dimension is examined. It is shown that the $\\star$-genvalue problem can be decomposed into separate harmonic oscillator equations for each dimension. The noncommutative plane is investigated in greater detail. The constraints for rotationally symmetric solutions and the corresponding two-dimensional harmonic oscillator are solved. The angular momentum operator is derived and its $\\star$-genvalue problem is shown to be equivalent to the usual eigenvalue problem. The $\\star$-genvalues for the angular momentum are found to depend on the energy difference of the oscillations in each dimension. Furthermore two examples of assymetric noncommutative harmonic oscillator are analysed. The first is the noncommutative two-dimensional Landau problem and the second is the three-dimensional harmonic oscillator with symmetrically noncommuting coordinates and momenta.
Quantum Energy Teleportation with a Linear Harmonic Chain
Nambu, Yasusada
2010-01-01
A protocol of quantum energy teleportation is proposed for a one-dimensional harmonic chain. A coherent-state POVM measurement is performed to coupled oscillators of the chain in the ground state accompanied by energy infusion to the system. This measurement consumes a part of ground state entanglement. Depending on the measurement result, a displacement operation is performed on a distant oscillator accompanied by energy extraction from the zero-point fluctuation of the oscillator. We find that the amount of consumed entanglement is bounded from below by a positive value that is proportional to the amount of teleported energy.
Institute of Scientific and Technical Information of China (English)
王德华; 李红艳; 马晓光; 王美山; 杨传路
2007-01-01
Using the periodic orbit theory, we computed the quantum level density of a particle in the two-dimensional harmonic oscillator potential with and without the magnetic flux line for different cases. Especially discuss the influence of the magnetic flux line on the quantum level density. The results show when the frequency ratio of the two-dimensional harmonic potential is a rational number, the quantum level density is discrete. Each peak in the level density corresponds to one energy. However, when the frequency ratio is an irrational number, the level density is oscillating, when the magnetic flux is added, the amplitude of the oscillation decreased. This can be considered as a consequence of Aharonov-Bohm effect.%利用周期轨道理论,我们计算了在不同情况下,一个粒子在二维谐振子势中存在和不存在磁通量时的量子能级密度.重点讨论了磁通量对量子能级密度的影响.计算结果表明:当二维谐振子势的频率比值是有理数时,量子能级是分立的,能级密度中的每一条峰正好对应一个量子能级.然而,当频率比是无理数时,能级密度发生振荡,当加上磁通量后,振荡减小.这可以看作是Aharonov-Bohm效应的结果.
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
P K Bera; J Datta
2006-12-01
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this spectral inverse method.
A Look at Damped Harmonic Oscillators through the Phase Plane
Daneshbod, Yousef; Latulippe, Joe
2011-01-01
Damped harmonic oscillations appear naturally in many applications involving mechanical and electrical systems as well as in biological systems. Most students are introduced to harmonic motion in an elementary ordinary differential equation (ODE) course. Solutions to ODEs that describe simple harmonic motion are usually found by investigating the…
Hamiltonian of mean force and a damped harmonic oscillator in an anisotropic medium
Jafari, Marjan; Kheirandish, Fardin
2017-01-01
The quantum dynamics of a damped harmonic oscillator is investigated in the presence of an anisotropic heat bath. The medium is modeled by a continuum of three dimensional harmonic oscillators and anisotropic coupling is treated by introducing tensor coupling functions. Starting from a classical Lagrangian, the total system is quantized in the framework of the canonical quantization. Following the Fano technique, the Hamiltonian of the system is diagonalized in terms of creation and annihilation operators that are linear combinations of the basic dynamical variables. Using the diagonalized Hamiltonian, the mean force internal energy, free energy and entropy of the damped oscillator are calculated.
A quantum parametric oscillator with trapped ions
Ding, Shiqian; Hablutzel, Roland; Loh, Huanqian; Matsukevich, Dzmitry
2015-01-01
A system of harmonic oscillators coupled via nonlinear interaction is a fundamental model in many branches of physics, from biophysics to electronics and condensed matter physics. In quantum optics, weak nonlinear interaction between light modes has enabled, for example, the preparation of squeezed states of light and generation of entangled photon pairs. While strong nonlinear interaction between the modes has been realized in circuit QED systems, achieving significant interaction strength on the level of single quanta in other physical systems remains a challenge. Here we experimentally demonstrate such interaction that is equivalent to photon up- and down-conversion using normal modes of motion in a system of two Yb ions. The nonlinearity is induced by the intrinsic anharmonicity of the Coulomb interaction between the ions and can be used to simulate fully quantum operation of a degenerate optical parametric oscillator. We exploit this interaction to directly measure the parity and Wigner functions of ion ...
Sanin, A.; Semyonov, E.
2012-01-01
Numerical integration of the non-stationary Schrödinger equation with Duffing potential depending on two coordinates has been carried out. Oscillation types and the influence of coupling between two oscillators on frequency spectra are analyzed in detail.
First harmonic injection locking of 24-GHz-oscillators
Directory of Open Access Journals (Sweden)
M. R. Kühn
2003-01-01
Full Text Available An increasing number of applications is proposed for the 24 GHz ISM-band, like automotive radar systems and short-range communication links. These applications demand for oscillators providing moderate output power of a few mW and moderate frequency stability of about 0.5%. The maximum oscillation frequency of low-cost off-theshelf transistors is too low for stable operation of a fundamental 24GHz oscillator. Thus, we designed a 24 GHz first harmonic oscillator, where the power generated at the fundamental frequency (12 GHz is reflected resulting in effective generation of output power at the first harmonic. We measured a radiated power from an integrated planar antenna of more than 1mW. Though this oscillator provides superior frequency stability compared to fundamental oscillators, for some applications additional stabilization is required. As a low-cost measure, injection locking can be used to phase lock oscillators that provide sufficient stability in free running mode. Due to our harmonic oscillator concept injection locking has to be achieved at the first harmonic, since only the antenna is accessible for signal injection. We designed, fabricated and characterized a harmonic oscillator using the antenna as a port for injection locking. The locking range was measured versus various parameters. In addition, phase-noise improvement was investigated. A theoretical approach for the mechanism of first harmonic injection locking is presented.
Coherent presentation of density operator of the harmonic oscillator in thermostat
Energy Technology Data Exchange (ETDEWEB)
Avakyan, R.M. [Department of Physics, Yerevan State University, 0025 Yerevan (Armenia); Hayrapetyan, A.G. [Institute of Applied Problems of Physics, National Academy of Sciences of Republic of Armenia, 0014 Yerevan (Armenia)], E-mail: armen@iapp.sci.am; Khachatryan, B.V.; Petrosyan, R.G. [Department of Physics, Yerevan State University, 0025 Yerevan (Armenia)
2007-12-10
Based on basis of the coherent states the density matrix of harmonic oscillator in thermostat is obtained. This method is mathematically refined and physically transparent for the interpretation of quantum phenomena in classical language. Such an approach gives an opportunity to easily find the density matrix in the multi-dimensional case.
Energy Technology Data Exchange (ETDEWEB)
Mota, R.D. [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, Mexico DF (Mexico)]. E-mail: mota@gina.esfm.ipn.mx; ravelo@esfm.ipn.mx; Granados, V.D.; Queijeiro, A.; Garcia, J. [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Mexico DF (Mexico)
2002-03-29
For the quantum two-dimensional isotropic harmonic oscillator we show that the Infeld-Hull radial operators, as well as those of the supersymmetric approach for the radial equation, are contained in the constants of motion of the problem. (author)
Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation
Institute of Scientific and Technical Information of China (English)
WANG Fei; QIAN Shang-Wu; FU Li-Ping; WANG Jing-Shan; GUO Ke-Tao
2008-01-01
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A genera/ equation for obtaining gauge-invariant transition probability amplitudes is derived.
Driven damped harmonic oscillator resonance with an Arduino
Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.
2017-07-01
In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.
A harmonic oscillator having “volleyball damping”
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Bound states of two-dimensional relativistic harmonic oscillators
Institute of Scientific and Technical Information of China (English)
Qiang Wen-Chao
2004-01-01
We give the exact normalized bound state wavefunctions and energy expressions of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.
The 3-Dimensional q-Deformed Harmonic Oscillator and Magic Numbers of Alkali Metal Clusters
Bonatsos, Dennis; Raychev, P P; Roussev, R P; Terziev, P A; Bonatsos, Dennis
1999-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3) > SOq(3) symmetry are compared to experimental data for alkali metal clusters, as well as to theoretical predictions of jellium models, Woods--Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. The 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry of systems of alkali metal clusters.
A new analytical approximation to the Duffing-harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Fesanghary, M. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States); Pirbodaghi, T. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of); Asghari, M. [School of Mechanical Engineering, Sharif University of Technology, Azadi Ave., 11365-9567 Tehran (Iran, Islamic Republic of)], E-mail: asghari@sharif.edu; Sojoudi, H. [Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803 (United States)
2009-10-15
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Directory of Open Access Journals (Sweden)
Wayne Cheng-Wei Huang
2013-01-01
Full Text Available Stochastic electrodynamics (SED predicts a Gaussian probability distribution for a classical harmonic oscillator in the vacuum field. This probability distribution is identical to that of the ground state quantum harmonic oscillator. Thus, the Heisenberg minimum uncertainty relation is recovered in SED. To understand the dynamics that give rise to the uncertainty relation and the Gaussian probability distribution, we perform a numerical simulation and follow the motion of the oscillator. The dynamical information obtained through the simulation provides insight to the connection between the classic double-peak probability distribution and the Gaussian probability distribution. A main objective for SED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of SED.
Coherent states for nonlinear harmonic oscillator and some of its properties
Energy Technology Data Exchange (ETDEWEB)
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Deformed Harmonic Oscillators for Metal Clusters and Balian-Bloch Theory
Bonatsos, D; Raychev, P P; Terziev, P A; Bonatsos, Dennis
2003-01-01
The predictions for the shell structure of metal clusters of the three-dimensional q-deformed harmonic oscillator (3D q-HO), utilizing techniques of quantum groups and having the symmetry Uq(3)$\\supset$SOq(3), are compared to the restrictions imposed by the periodic orbit theory of Balian and Bloch, of electrons moving in a spherical cavity. It is shown that agreement between the predictions of the two models is established through the introduction of an additional term to the Hamiltonian of the 3D q-HO, which does not influence the predictions for supershells. This term preserves the Uq(3)$\\supset$SOq(3) symmetry, while in addition it can be derived through a variational procedure, analogous to the one leading from the usual harmonic oscillator to the Morse oscillator by introducing the concept of the Variable Frequency Oscillator (VFO).
Dynamically self-regular quantum harmonic black holes
Directory of Open Access Journals (Sweden)
Euro Spallucci
2015-04-01
Full Text Available The recently proposed UV self-complete quantum gravity program is a new and very interesting way to envision Planckian/trans-Planckian physics. In this new framework, high energy scattering is dominated by the creation of micro black holes, and it is experimentally impossible to probe distances shorter than the horizon radius. In this letter we present a model which realizes this idea through the creation of self-regular quantum black holes admitting a minimal size extremal configuration. Their radius provides a dynamically generated minimal length acting as a universal short-distance cutoff. We propose a quantization scheme for this new kind of microscopic objects based on a Bohr-like approach, which does not require a detailed knowledge of quantum gravity. The resulting black hole quantum picture resembles the energy spectrum of a quantum harmonic oscillator. The mass of the extremal configuration plays the role of zero-point energy. Large quantum number re-establishes the classical black hole description. Finally, we also formulate a “quantum hoop conjecture” which is satisfied by all the mass eigenstates and sustains the existence of quantum black holes sourced by Gaussian matter distributions.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Violation of smooth observable macroscopic realism in a harmonic oscillator.
Leshem, Amir; Gat, Omri
2009-08-14
We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.
Golden Quantum Oscillator and Binet-Fibonacci Calculus
Pashaev, Oktay K
2011-01-01
The Binet-Fibonacci formula for Fibonacci numbers is treated as a q-number (and q-operator) with Golden ratio bases $q=\\phi$ and $Q=-1/\\phi$. Quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given just by Fibonacci numbers. Ratio of successive energy levels is found as the Golden sequence and for asymptotic states it appears as the Golden ratio. This why we called this oscillator as the Golden oscillator. By double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived.
Maireche Abdelmadjid
2015-01-01
In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two in...
Upper quantum Lyapunov exponent and parametric oscillators
Jauslin, H. R.; Sapin, O.; Guérin, S.; Wreszinski, W. F.
2004-11-01
We introduce a definition of upper Lyapunov exponent for quantum systems in the Heisenberg representation, and apply it to parametric quantum oscillators. We provide a simple proof that the upper quantum Lyapunov exponent ranges from zero to a positive value, as the parameters range from the classical system's region of stability to the instability region. It is also proved that in the instability region the parametric quantum oscillator satisfies the discrete quantum Anosov relations defined by Emch, Narnhofer, Sewell, and Thirring.
An application of the three-dimensional q-deformed harmonic oscillator to the shell model
Energy Technology Data Exchange (ETDEWEB)
Raychev, P.P. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy); Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Roussev, R.P.; Terziev, P.A. [Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 72 Tzarigrad Road, BG-1784 Sofia (Bulgaria); Lo Iudice, N. [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , Monte S Angelo, via Cintia, I-80125 Napoli (Italy)
1998-10-01
A procedure for the construction of a q-deformed version of the Hamiltonian of the three-dimensional harmonic oscillator (HO), based on the application of q-deformed algebras, is presented. The spectrum of this Hamiltonian is not degenerated in the quantum number of the q-deformed angular momentum. The results together with their applicability to the shell model are compared with the predictions of the modified HO. (author)
Solution to the Master Equation of a Free Damped Harmonic Oscillator with Linear Driving
Institute of Scientific and Technical Information of China (English)
杨洁; 逯怀新; 赵博; 赵梅生; 张永德
2003-01-01
We use the Lie algebra representation theory for superoperators to solve the master equation for a harmonic oscillator with a linear driving term in a squeezed thermal reservoir. By using the quantum displacement transformation and squeeze transformation, we show that the master equation has an su(1, 1) Lie algebra structure,with which we obtain the explicit solution to the master equation. A simple but typical example is given to illustrate our method.
On a q-extension of the linear harmonic oscillator with the continuous orthogonality property on ℝ
Alvarez-Nodarse, R.; Atakishiyeva, M. K.; Atakishiyev, N. M.
2005-11-01
We discuss a q-analogue of the linear harmonic oscillator in quantum mechanics based on a q-extension of the classical Hermite polynomials H n ( x) recently introduced by us in R. Alvarez-Nodarse et al.: Boletin de la Sociedad Matematica Mexicana (3) 8 (2002) 127. The wave functions in this q-model of the quantum harmonic oscillator possess the continuous orthogonality property on the whole real line ℝ with respect to a positive weight function. A detailed description of the corresponding q-system is carried out.
On harmonic oscillators and their Kemmer relativistic forms
Debergh, Nathalie; Beckers, Jules
1993-01-01
It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearit...
Simulating Harmonic Oscillator and Electrical Circuits: A Didactical Proposal
Albano, Giovannina; D'Apice, Ciro; Tomasiello, Stefania
2002-01-01
A Mathematica[TM] package is described that uses simulations and animations to illustrate key concepts in harmonic oscillation and electric circuits for students not majoring in physics or mathematics. Students are not required to know the Mathematica[TM] environment: a user-friendly interface with buttons functionalities and on-line help allows…
A Simple Mechanical Model for the Isotropic Harmonic Oscillator
Nita, Gelu M.
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)
Exact complex integrals in two dimensions for shifted harmonic oscillators
Indian Academy of Sciences (India)
Jasvinder Singh Virdi; S C Mishra
2012-07-01
We use rationalization method to study two-dimensional complex dynamical systems (shifted harmonic oscillator in complex plane) on the extended comples phase space (ECPS). The role and scope of the derived invatiants in the context of various physical problems are high-lighted.
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
The harmonic oscillator, dimensional analysis and inflationary solutions
San Costa, S
2002-01-01
In this work, focused on the production of exact inflationary solutions using dimensional analysis, it is shown how to explain inflation from a pragmatic and basic point of view, in a step-by-step process, starting from the one-dimensional harmonic oscillator.
Low Noise Second Harmonic Oscillator Using Mutually Synchronized Gunn Diodes
Kawasaki, Kengo; Tanaka, Takayuki; Aikawa, Masayoshi
This paper represents a low noise second harmonic oscillator using mutually synchronized Gunn diodes. A multi-layer MIC technology is adopted to reduce the circuit size of the oscillator. The oscillator consists of Gunn diodes, slot line resonators and strip lines. By embedding Gunn diodes in the slot line resonators, a harmonic RF signal can be generated very easily. The strip lines are used for the power combining output circuit. The shape of slot line resonator is square in order to achieve the low phase noise and the suppression of undesired harmonics. The second harmonic oscillator is designed and fabricated in K band. The output power is +8.89dBm at the design frequency of 18.75GHz (2f0) with the phase noise of -116.2dBc/Hz at the offset frequency of 1MHz. Excellent suppression of the undesired fundamental frequency signal (f0) of -33dBc is achieved. Also, the circuit size is reduced by three-tenths relative to that of the previously proposed circuit.
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
Optical realization of the dissipative quantum oscillator
Longhi, Stefano
2016-01-01
An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of the time-dependent Caldirola-Kanai Hamiltonian of the dissipative quantum oscillator, and enables to visualize the effects of damped oscillations in the classical (ray optics) limit and wave packet collapse in the quantum (wave optics) regime.
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.
Quantum coherent oscillations in the early universe
Pikovski, Igor
2015-01-01
Cosmic inflation is commonly assumed to be driven by quantum fields. Quantum mechanics predicts phenomena such as quantum fluctuations and tunneling of the field. Here we show an example of a quantum interference effect which goes beyond the semi-classical treatment and which may be of relevance in the early universe. We study the quantum coherent dynamics for a tilted, periodic potential, which results in genuine quantum oscillations of the inflaton field, analogous to Bloch oscillations in condensed matter and atomic systems. Our results show that quantum interference phenomena may be of relevance in cosmology.
Dynamically self-regular quantum harmonic black holes
Spallucci, Euro
2015-01-01
The recently proposed UV self-complete quantum gravity program is a new and very interesting way to envision Planckian/trans-Planckian physics. in this new framework, high energy scattering is dominated by the creation of micro black holes, and it is experimentally impossible to probe distances shorter than the horizon radius. In this letter we present a model which realizes this idea through the creation of self-regular quantum black holes admitting a minimal size extremal configuration. Their radius provides a dynamically generated minimal length acting as a universal short-distance cut-off. We propose a quantisation scheme for this new kind of microscopic objects based on a Bohr-like approach, which does not require a detailed knowledge of quantum gravity. The resulting black hole quantum picture resembles the energy spectrum of a quantum harmonic oscillator. The mass of the extremal configuration plays the role of zero-point energy. Large quantum number re-establish the classical black hole description. F...
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.
Classical oscillators in the control of quantum tunneling: Numerical experiments
Kar, Susmita; Bhattacharyya, S. P.
2016-06-01
The dynamics of a classical anharmonic oscillator is exploited to control the tunneling dynamics of a quantum particle to which the classical oscillator is coupled. The mixed quantum classical problem is investigated at a mean-field like level. The anharmonic strength (λ) , particle mass (Mc) and harmonic stiffness (ωc) of the classical controller are explored as possible control parameters for the tunneling dynamics. The strength, the type of coupling between the quantum system and classical controller and the effective frequency of the controller emerge as crucial factors in shaping the nature and extent of the control. A whole spectrum of possibilities starting from enhancement, suppression to complete destruction of tunneling emerge depending on values assigned to the control parameters, the type of coupling and the control configuration used. When classical controller is replaced by a quantum controller, the control landscape becomes much simpler.
Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
Chen, Xi
2010-01-01
There is recently a surge of interest to cut down the time it takes to change the state of a quantum system adiabatically. We study for the time-dependent harmonic oscillator the transient energy excitation in speed-up processes designed to reproduce the initial populations at some predetermined final frequency and time, providing lower bounds and examples. Implications for the limits imposed to the process times and for the principle of unattainability of the absolute zero, in a single expansion or in quantum refrigerator cycles, are drawn.
Quantum state transfer via Bloch oscillations.
Tamascelli, Dario; Olivares, Stefano; Rossotti, Stefano; Osellame, Roberto; Paris, Matteo G A
2016-05-18
The realization of reliable quantum channels, able to transfer a quantum state with high fidelity, is a fundamental step in the construction of scalable quantum devices. In this paper we describe a transmission scheme based on the genuinely quantum effect known as Bloch oscillations. The proposed protocol makes it possible to carry a quantum state over different distances with a minimal engineering of the transmission medium and can be implemented and verified on current quantum technology hardware.
Entanglement Dynamics of Quantum Oscillators Nonlinearly Coupled to Thermal Environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2014-01-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing and coupling strength, is compared to results for systems with linear system-reservoir coupling. We fin...
Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Pascual, Carolina [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-11-19
The first-order harmonic balance method via the first Fourier coefficient is used to construct two approximate frequency-amplitude relations for the relativistic oscillator for which the nonlinearity (anharmonicity) is a relativistic effect due to the time line dilation along the world line. Making a change of variable, a new nonlinear differential equation is obtained and two procedures are used to approximately solve this differential equation. In the first the differential equation is rewritten in a form that does not contain a square-root expression, while in the second the differential equation is solved directly. The approximate frequency obtained using the second procedure is more accurate than the frequency obtained with the first due to the fact that, in the second procedure, application of the harmonic balance method produces an infinite set of harmonics, while in the first procedure only two harmonics are produced. Both approximate frequencies are valid for the complete range of oscillation amplitudes, and excellent agreement of the approximate frequencies with the exact one are demonstrated and discussed. The discrepancy between the first-order approximate frequency obtained by means of the second procedure and the exact frequency never exceeds 1.6%. We also obtained the approximate frequency by applying the second-order harmonic balance method and in this case the relative error is as low 0.31% for all the range of values of amplitude of oscillation A.
Manipulating Fock states of a harmonic oscillator while preserving its linearity
Juliusson, K.; Bernon, S.; Zhou, X.; Schmitt, V.; le Sueur, H.; Bertet, P.; Vion, D.; Mirrahimi, M.; Rouchon, P.; Esteve, D.
2016-12-01
We present a scheme for controlling the quantum state of a harmonic oscillator by coupling it to an anharmonic multilevel system (MLS) with first- to second-excited-state transition on resonance with the oscillator. In this scheme, which we call ef-resonant, the spurious oscillator Kerr nonlinearity inherited from the MLS is very small, while its Fock states can still be selectively addressed via an MLS transition at a frequency that depends on the number of photons. We implement this concept in a circuit-QED setup with a microwave three-dimensional cavity (the oscillator, with frequency 6.4 GHz and quality factor QO=2 ×106 ) embedding a frequency tunable transmon qubit (the MLS). We characterize the system spectroscopically and demonstrate selective addressing of Fock states and a Kerr nonlinearity below 350 Hz. At times much longer than the transmon coherence times, a nonlinear cavity response with driving power is also observed and explained.
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
Quantum noise-induced chaotic oscillations
Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Quantum noise-induced chaotic oscillations
Bag, B C; Bag, Bidhan Chandra; Ray, Deb Shankar
1999-01-01
We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxilliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.
Dynamics of Coupled Quantum-Classical Oscillators
Institute of Scientific and Technical Information of China (English)
HE Wei-Zhong; XU Liu-Su; ZOU Feng-Wu
2004-01-01
@@ The dynamics of systems consisting of coupled quantum-classical oscillators is numerically investigated. It is shown that, under certain conditions, the quantum oscillator exhibits chaos. When the mass of the classical oscillator increases, the chaos will be suppressed; if the energy of the system and/or the coupling strength between the two oscillators increases, chaotic behaviour of the system appears. This result will be helpful to understand the probability of the emergence of quantum chaos and may be applied to explain the spectra of complex atoms qualitatively.
Directory of Open Access Journals (Sweden)
Sameer M. Ikhdair
2013-01-01
Full Text Available The Klein-Gordon (KG equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ=0 cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.
Non- Markovian Quantum Stochastic Equation For Two Coupled Oscillators
Alpomishev, E X
2016-01-01
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical expressions for transport coefficients was found. Generalized Langevin equations and fluctuation-dissipation relations are derived for the case of a nonlinear non-Markovian noise. The explicit expressions for the time-dependent friction and diffusion coefficients are presented for the case of linear couplings in the coordinate between the collective two coupled harmonic oscillators and heat bath.
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
Second-harmonic imaging of semiconductor quantum dots
DEFF Research Database (Denmark)
Østergaard, John Erland; Bozhevolnyi, Sergey I.; Pedersen, Kjeld;
2000-01-01
Resonant second-harmonic generation is observed at room temperature in reflection from self-assembled InAlGaAs quantum dots grown on a GaAs (001) substrate. The detected second-harmonic signal peaks at a pump wavelength of similar to 885 nm corresponding to the quantum-dot photoluminescence maximum....... In addition, the second-harmonic spectrum exhibits another smaller but well-pronounced peak at 765 nm not found in the linear experiments. We attribute this peak to the generation of second-harmonic radiation in the AlGaAs spacer layer enhanced by the local symmetry at the quantum-dot interface. We further...... observe that second-harmonic images of the quantum-dot surface structure show wavelength-dependent spatial variations. Imaging at different wavelength is used to demonstrate second-harmonic generation from the semiconductor quantum dots. (C) 2000 American Institute of Physics....
Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator
Directory of Open Access Journals (Sweden)
Mohammad Heydari
2014-01-01
Full Text Available A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method.
Reaching Synchronization in Networked Harmonic Oscillators With Outdated Position Data.
Song, Qiang; Yu, Wenwu; Cao, Jinde; Liu, Fang
2016-07-01
This paper studies the synchronization problem for a network of coupled harmonic oscillators by proposing a distributed control algorithm based only on delayed position states, i.e., outdated position states stored in memory. The coupling strength of the network is conveniently designed according to the absolute values and the principal arguments of the nonzero eigenvalues of the network Laplacian matrix. By analyzing a finite number of stability switches of the network with respect to the variation in the time delay, some necessary and sufficient conditions are derived for reaching synchronization in networked harmonic oscillators with positive and negative coupling strengths, respectively, and it is shown that the time delay should be taken from a set of intervals bounded by some critical values. Simulation examples are given to illustrate the effectiveness of the theoretical analysis.
Anisotropic Harmonic Oscillator in a Static Electromagnetic Field
Institute of Scientific and Technical Information of China (English)
LIN Qiong-Gui
2002-01-01
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail.
An analogue of the Berry phase for simple harmonic oscillators
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Harmonic oscillator Floquet states in the Bargmann-Segal space
Energy Technology Data Exchange (ETDEWEB)
Palma, A. [Instituto Nacional de Astrofisica, Optica y Electronica (INAOE), Puebla (Mexico)]. E-mail: palma@sirio.ifuap.buap.mx; Leon, V. [Instituto de Fisica, BUAP, Puebla (Mexico); Lefebvre, R. [Laboratoire de Photophysique Moleculaire du CNRS, Universite Paris-Sud, Orsay (France); UFR de Physique Fondamentale et Appliquee, Universite Pierre et Marie Curie, Paris (France)
2002-01-18
The Floquet quasi-energies and eigenfunctions for the harmonic oscillator interacting with a monochromatic electric field are obtained by using the so-called Bargmann-Segal space. The Schroedinger second-order differential equation in configuration space is transformed into a linear first-order equation in such a space, which is easily solved by means of an auxiliary system (called the Lagrange system) of ordinary differential equations. This method compares favourably with others previously used. (author)
A type of perturbation of the harmonic oscillator
López, Jesús A Álvarez
2011-01-01
Consider perturbations of the harmonic oscillator $H$ of the form $P=H-f_1\\frac{d}{dx}+f_2$ for functions $f_1$ and $f_2$. If $f_2$ can be given as certain expression of $f_1$ and a parameter $\\sigma>-1$, then many well known properties of $H$ are generalized to $P$: self-adjointness in the appropriate Hilbert space, description of the spectrum, recurrence formula for the eigenfunctions, eigenfunction estimates and embedding results.
Coherent and squeezed states for the 3D harmonic oscillator
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
2017-01-01
A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.
Teaching from a Microgravity Environment: Harmonic Oscillator and Pendulum
Benge, Raymond; Young, Charlotte; Davis, Shirley; Worley, Alan; Smith, Linda; Gell, Amber
2009-04-01
This presentation reports on an educational experiment flown in January 2009 as part of NASA's Microgravity University program. The experiment flown was an investigation into the properties of harmonic oscillators in reduced gravity. Harmonic oscillators are studied in every introductory physics class. The equation for the period of a harmonic oscillator does not include the acceleration due to gravity, so the period should be independent of gravity. However, the equation for the period of a pendulum does include the acceleration due to gravity, so the period of a pendulum should appear longer under reduced gravity (such as lunar or Martian gravity) and shorter under hyper-gravity. These environments can be simulated aboard an aircraft. Video of the experiments being performed aboard the aircraft is to be used in introductory physics classes. Students will be able to record information from watching the experiment performed aboard the aircraft in a similar manner to how they collect data in the laboratory. They can then determine if the experiment matches theory. Video and an experimental procedure are being prepared based upon this flight, and these materials will be available for download by faculty anywhere with access to the internet who wish to use the experiment in their own classrooms.
Energy Technology Data Exchange (ETDEWEB)
Guasti, M Fernandez [Depto de Fisica, CBI, Universidad A Metropolitana - Iztapalapa, 09340 Mexico, DF, Apdo Postal 55-534 (Mexico); Moya-Cessa, H [INAOE, Coordinacion de Optica, Apdo Postal 51 y 216, 72000 Puebla, Pue. (Mexico)
2003-02-28
An extension of the classical orthogonal functions invariant to the quantum domain is presented. This invariant is expressed in terms of the Hamiltonian. Unitary transformations which involve the auxiliary function of this quantum invariant are used to solve the time-dependent Schroedinger equation for a harmonic oscillator with time-dependent parameter. The solution thus obtained is in agreement with the results derived using other methods which invoke the Lewis invariant in their procedures.
Institute of Scientific and Technical Information of China (English)
Sameer M.Ikhdair; Majid Hamzavi
2012-01-01
We study the effects of the perpendicular magnetic and Aharonov Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein-Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO).We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter,magnetic field strength,AB flux field,and magnetic quantum number by means of the Nikiforov-Uvarov (NU) method.The non-relativistic limit,PHO,and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
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)
The quantum measurement approach to particle oscillations
Anastopoulos, C
2010-01-01
The LSND and MiniBoone seeming anomalies in neutrino oscillations are usually attributed to physics beyond the Standard model. It is, however, possible that they may be an artefact of the theoretical treatment of particle oscillations that ignores fine points of quantum measurement theory relevant to the experiments. In this paper, we construct a rigorous measurement-theoretic framework for the description of particle oscillations, employing no assumptions extrinsic to quantum theory. The formalism leads to a non-standard oscillation formula; at low energy it predicts an `anomalous' oscillation wavelength, while at high energy it differs from the standard expression by a factor of 2. The key novelties in the formalism are the treatment of a particle's time of arrival at the detector as a genuine quantum observable, the theoretical precision in the definition of quantum probabilities, and the detailed modeling of the measurement process. The article also contains an extensive critical review of existing theore...
Chih-Chun Chang; Guang-Yin Chen; Lee Lin
2016-01-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero a...
From ordinary to discrete quantum mechanics: The Charlier oscillator and its coalgebra symmetry
Latini, D.; Riglioni, D.
2016-10-01
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.
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...... oscillator strength due to Coulomb effects. This is in stark contrast to the measured oscillator strength, which turns out to be so small that it can be described by excitons in the strong confinement regime. We attribute these findings to exciton localization in local potential minima arising from alloy...
A simple harmonic balance method for solving strongly nonlinear oscillators
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
Effective field theory in the harmonic oscillator basis
Binder, S.; Ekström, A.; Hagen, G.; Papenbrock, T.; Wendt, K. A.
2016-04-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. In oscillator EFT, matrix elements of EFTs formulated for continuous momenta are evaluated at the discrete momenta that stem from the diagonalization of the kinetic energy in the finite oscillator space. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn converge fast for the ground-state energies and radii in feasible model spaces.
Rosu, H. C.; Khmelnytskaya, K. V.
2011-09-01
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned.
Rosu, H C
2010-01-01
Previous research made us consider a simple but curious problem related to the kind of oscillators that are produced in the usual supersymmetric scheme when one introduces a constant shift of the Riccati solution R(t)=-omega _0 tan(omega _0t) of the classical harmonic oscillator. The corresponding mathematical scheme is presented in detail showing that at least some of these oscillators could be of physical nature. We give the solutions of the resulting second-order differential equations obtaining the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry
Indian Academy of Sciences (India)
Rajarshi Chakrabarti
2009-04-01
Based on a Hamiltonian description we present a rigorous derivation of the transient state work fluctuation theorem and the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics dissipative. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not restricted only to the Ohmic bath, rather it is more general, for a non-Ohmic bath. We also derive expressions of the average work done and the variance of the work done in terms of the two-time correlation function of the fluctuations of the position of the harmonic oscillator. In the case of an Ohmic bath, we use these relations to evaluate the average work done and the variance of the work done analytically and verify the transient state work fluctuation theorem quantitatively. Actually these relations have far-reaching consequences. They can be used to numerically evaluate the average work done and the variance of the work done in the case of a non-Ohmic bath when analytical evaluation is not possible.
Detecting the harmonics of oscillations with time-variable frequencies
Sheppard, L. W.; Stefanovska, A.; McClintock, P. V. E.
2011-01-01
A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology.
Steuernagel, Ole
2014-06-01
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us to understand either from the viewpoint of the other. Here we show that all general time-dependent solutions of the free-particle Schrödinger equation can be mapped to solutions of the Schrödinger equation for harmonic potentials, both the trapping oscillator and the inverted "oscillator". This map is fully invertible and therefore induces an isomorphism between both types of system, they are equivalent. A composition of the map and its inverse allows us to map from one harmonic oscillator to another with a different spring constant and different center position. The map is independent of the state of the system, consisting only of a coordinate transformation and multiplication by a form factor, and can be chosen such that the state is identical in both systems at one point in time. This transition point in time can be chosen freely, the wave function of the particle evolving in time in one system before the transition point can therefore be linked up smoothly with the wave function for the other system and its future evolution after the transition point. Such a cut-and-paste procedure allows us to describe the instantaneous changes of the environment a particle finds itself in. Transitions from free to trapped systems, between harmonic traps of different spring constants or center positions, or, from harmonic binding to repulsive harmonic potentials are straightforwardly modelled. This includes some time-dependent harmonic potentials. The mappings introduced here are computationally more efficient than either state-projection or harmonic oscillator propagator techniques conventionally employed when describing instantaneous (non-adiabatic) changes of a quantum particle's environment.
Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations
Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R
2016-01-01
Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...
A dynamical systems approach to Bohmian trajectories in a 2D harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Borondo, F [Departamento de Quimica, and Instituto Mixto de Ciencias Matematicas CSIC-UAM-UC3M-UCM, Universidad Autonoma de Madrid, Cantoblanco-28049 Madrid (Spain); Luque, A; Villanueva, J [Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, 08028 Barcelona (Spain); Wisniacki, D A [Departamento de Fisica ' J. J. Giambiagi' , FCEN, UBA, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires (Argentina)], E-mail: f.borondo@uam.es, E-mail: alejandro.luque@upc.edu, E-mail: jordi.villanueva@upc.edu, E-mail: wisniacki@df.uba.ar
2009-12-11
Vortices are known to play a key role in the dynamics of the quantum trajectories defined within the framework of the de Broglie-Bohm formalism of quantum mechanics. It has been rigourously proved that the motion of a vortex in the associated velocity field can induce chaos in these trajectories, and numerical studies have explored the rich variety of behaviors that due to their influence can be observed. In this paper, we go one step further and show how the theory of dynamical systems can be used to construct a general and systematic classification of such dynamical behaviors. This should contribute to establish some firm grounds on which the studies on the intrinsic stochasticity of Bohm's quantum trajectories can be based. An application to the two-dimensional isotropic harmonic oscillator is presented as an illustration.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Departamento de Matematicas, Centro de Investigacion y de Estudios Avenzados del IPN, 07000, Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Queijeiro, A [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Garcia, J [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico); Guzman, L [Unidad Profesional Interdisciplinaria en Ingenieria y Tecnologias Avanzadas, IPN Av. Instituto Politecnico Nacional No 2580, Col. La Laguna Ticoman, Delegacion Gustavo A Madero, CP 07340 Mexico DF (Mexico)
2003-05-02
We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method.
Quantum oscillations in organic metals and superconductors
Energy Technology Data Exchange (ETDEWEB)
Clayton, N
2000-12-01
De Haas-van Alphen (dHvA) oscillations have been observed in the organic superconductor {kappa}-(BEDT-TTF){sub 2}Cu(NCS){sub 2} at temperatures down to 30 mK, and the oscillations are found to suffer an additional attenuation, R{sub s}, in the mixed state. None of the theoretical models, coupled with the mean-field expression for the field-dependence of the superconducting energy gap, {delta}, offer a good fit to the data. By including the effects of thermal fluctuations in the field-dependence of {delta}, a reasonable fit to the data can be made at the lowest temperatures. However, the form of the damping does not change appreciably as the temperature is increased up to 560 mK, which is inconsistent with the thermal fluctuation model. Angle resolved dHvA measurements on {kappa}-(BEDT-TTF){sub 2}Cu(NCS){sub 2} have allowed R{sub s} curves to be measured as a function of the orientation of the applied magnetic field. These R{sub s}({theta}) curves may be scaled onto one another by taking the components of the magnetic fields perpendicular to the layers. The scale of the fluctuations is independent of angle within experimental errors. This, and an angle-independent normal state Dingle temperature, suggests that the quasiparticle orbits are confined to the two-dimensional layers for all angles of applied magnetic field. An angle resolved dHvA study has been performed on the organic metal {alpha}-(BEDT-TTF){sub 2}KHg(NCS){sub 4}. At low temperatures and low fields, the Fermi surface is reconstructed in this material, and the dHvA signal is dominated by an a frequency and its second harmonic, 2{alpha}. The amplitude of the 2{alpha} frequency is shown to deviate from the predictions of the Lifshitz-Kosevich expression, but is found to be consistent with a 'frequency doubling' mechanism. In this scheme, the 2{alpha} frequency arises from a new type of quantum oscillatory phenomenon, due to the susceptibility of the quasi one-dimensional sheets, driven by
Anisotropic Harmonic Oscillator in s Static Electromagnetic Field
Institute of Scientific and Technical Information of China (English)
LINQiong－Gui
2002-01-01
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied.Several configurations of the electromagnetic field are considered.The Schoedinger equation is solved analytically in most of the cases.The energy levels and wave functions are obtained explicitly.In some of the cases,the ground state obtained is not a minimum wave packet,though it is of the Gaussian type.Coherent and squeezed states and their time evolution are discussed in detail.
Harmonic response of a class of finite extensibility nonlinear oscillators
Febbo, M.
2011-06-01
Finite extensibility oscillators are widely used to simulate those systems that cannot be extended to infinity. For example, they are used when modelling the bonds between molecules in a polymer or DNA molecule or when simulating filaments of non-Newtonian liquids. In this paper, the dynamic behavior of a harmonically driven finite extensibility oscillator is presented and studied. To this end, the harmonic balance method is applied to determine the amplitude-frequency and amplitude-phase equations. The distinguishable feature in this case is the bending of the amplitude-frequency curve to the frequency axis, making it asymptotically approach the limit of maximum elongation of the oscillator, which physically represents the impossibility of the system reaching this limit. Also, the stability condition that defines stable and unstable steady-state solutions is derived. The study of the effect of the system parameters on the response reveals that a decreasing value of the damping coefficient or an increasing value of the excitation amplitude leads to the appearance of a multi-valued response and to the existence of a jump phenomenon. In this sense, the critical amplitude of the excitation, which means here a certain value of external excitation that results in the occurrence of jump phenomena, is also derived. Numerical experiments to observe the effects of system parameters on the frequency-amplitude response are performed and compared with analytical calculations. At a low value of the damping coefficient or at a high value of excitation amplitude, the agreement is poor for low frequencies but good for high frequencies. It is demonstrated that the disagreement is caused by the neglect of higher-order harmonics in the analytical formulation. These higher-order harmonics, which appear as distinguishable peaks at certain values in the frequency response curves, are possible to calculate considering not the linearized frequency of the oscillator but its actual
Effective field theory in the harmonic-oscillator basis
Binder, S; Hagen, G; Papenbrock, T; Wendt, K A
2015-01-01
We develop interactions from chiral effective field theory (EFT) that are tailored to the harmonic oscillator basis. As a consequence, ultraviolet convergence with respect to the model space is implemented by construction and infrared convergence can be achieved by enlarging the model space for the kinetic energy. We derive useful analytical expressions for an exact and efficient calculation of matrix elements. By fitting to realistic phase shifts and deuteron data we construct an effective interaction from chiral EFT at next-to-leading order. Many-body coupled-cluster calculations of nuclei up to 132Sn exhibit a fast convergence of ground-state energies and radii in feasible model spaces.
Quantum oscillations of nitrogen atoms in uranium nitride
Aczel, A. A.; Granroth, G. E.; MacDougall, G. J.; Buyers, W. J. L.; Abernathy, D. L.; Samolyuk, G. D.; Stocks, G. M.; Nagler, S. E.
2012-10-01
The vibrational excitations of crystalline solids corresponding to acoustic or optic one-phonon modes appear as sharp features in measurements such as neutron spectroscopy. In contrast, many-phonon excitations generally produce a complicated, weak and featureless response. Here we present time-of-flight neutron scattering measurements for the binary solid uranium nitride, showing well-defined, equally spaced, high-energy vibrational modes in addition to the usual phonons. The spectrum is that of a single atom, isotropic quantum harmonic oscillator and characterizes independent motions of light nitrogen atoms, each found in an octahedral cage of heavy uranium atoms. This is an unexpected and beautiful experimental realization of one of the fundamental, exactly solvable problems in quantum mechanics. There are also practical implications, as the oscillator modes must be accounted for in the design of generation IV nuclear reactors that plan to use uranium nitride as a fuel.
A method of solving simple harmonic oscillator Schroedinger equation
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Quantum groups, deformed oscillators and their interrelations
Damaskinsky, E V; Damaskinsky, E V; Kulish, P P
1995-01-01
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: GL_q(2), sl_q(2), q-oscillator algebra {\\cal A}(q), and reflection equation algebra. The Gauss decompositions of quantum groups and their realizations in terms of\\, {\\cal A}(q) are given.
The two capacitor problem revisited: simple harmonic oscillator model approach
Lee, Keeyung
2012-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that \\emph {exactly half} the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be \\emph {exactly half} the supplied energy whether that is caused by the Joule heat or by the radiation. This paper which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem is suitable for all undergraduate...
Dynamical Recurrence and the Quantum Control of Coupled Oscillators
Genoni, Marco G.; Serafini, Alessio; Kim, M. S.; Burgarth, Daniel
2012-04-01
Controllability—the possibility of performing any target dynamics by applying a set of available operations—is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, such as spin systems, precise criteria to establish controllability, such as the so-called rank criterion, are well known. However, most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems—encompassing quantum light, ensembles of bosonic atoms, motional degrees of freedom of ions, and nanomechanical oscillators—governed by quadratic Hamiltonians (such that their evolution is analogous to coupled harmonic oscillators). After having highlighted the intimate connection between controllability and recurrence in the Hilbert space, we prove that, for coupled oscillators, a simple extra condition has to be fulfilled to extend the rank criterion to infinite-dimensional quadratic systems. Further, we present a useful application of our finding, by proving indirect controllability of a chain of harmonic oscillators.
Chang, Chih-Chun; Chen, Guang-Yin; Lin, Lee
2016-11-01
We investigate a system of an array of N simple harmonic oscillators (SHO) interacting with photons through QED interaction. As the energy of photon is around the spacing between SHO energy levels, energy gaps appear in the dispersion relation of the interacted (dressed) photons. This is quite different from the dispersion relation of free photons. Due to interactions between dressed photonic field and arrayed SHO, the photoresistance of this system shows oscillations and also drops to zero as irradiated by EM field of varying frequencies.
The sojourn time of the inverted harmonic oscillator on the noncommutative plane
Energy Technology Data Exchange (ETDEWEB)
Guo Guangjie; Ren Zhongzhou; Ju Guoxing [Department of Physics, Nanjing University, Nanjing 210093 (China); Long Chaoyun, E-mail: woggj@126.com [Department of Physics, Guizhou University, Guiyang 550025 (China)
2011-10-21
The sojourn time of the Gaussian wavepacket that is stationed at the center of the inverted harmonic oscillator is investigated on the noncommutative plane in detail. In ordinary commutative space quantum mechanics, the sojourn time of the Gaussian wavepacket is always a monotonically decreasing function of the curvature parameter {omega} of the potential. However, in this paper, we find that the spatial noncommutativity makes the sojourn time a concave function of {omega} with a minimum at an inflection point {omega}{sub 0}. Furthermore, if {omega} is larger than a certain critical value the sojourn time will become infinity. Thus, the ordinary intuitive physical picture about the relation between the sojourn time and the shape of the inverted oscillator potential is changed when the spatial noncommutativity is considered. (paper)
Observation of harmonic gyro-backward-wave oscillation in a 100 GHz CARM oscillator experiment
McCowan, Robert B.; Sullivan, Carol A.; Gold, Steven H.; Fliflet, Arne W.
1991-02-01
A cyclotron autoresonance maser (CARM) oscillator experiment is reported, using a 600 keV, 200 A electron beam, and a whispering gallery-mode rippled-wall Bragg cavity. This device was designed to produce tens of megawatts of radiation at 100 GHz from a CARM interaction, but instead has produced only moderate powers (tens of kWs) in fundamental gyrotron modes near 35 GHz, in third-harmonic-gyro-BWO modes, and possible third-harmonic gyrotron modes at frequencies near the expected CARM frequency, with no discernable CARM radiation. The lack of observable CARM radiation is attributed to excessive ripple on the voltage waveform and to mode competition. Calculations of the spectrum and growth rate of the backward-wave oscillations are consistent with the experimental observation.
Directory of Open Access Journals (Sweden)
P. A. Deymier
2016-12-01
Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Deymier, P. A.; Runge, K.; Vasseur, J. O.
2016-12-01
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
The Klauder-Daubechies Construction of the Phase Space Path Integral and the Harmonic Oscillator
Govaerts, Jan; Mattelaer, Olivier
2009-01-01
The canonical operator quantisation formulation corresponding to the Klauder-Daubechies construction of the phase space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularisation parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularisation of short distance divergences, keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems.
Institute of Scientific and Technical Information of China (English)
CHEN CHANG-YUAN
2000-01-01
In this paper, the general formulas and the recurrence formulas for radial matrix elements of N-dimensional isotropic harmonic oscillator are obtained. The relevant results of 2- dimensional and 3- dimensiona] isotropic harmonic oscillators reported in the reference papers are contained in a more general equations derived in this paper as special cases.
An application of the 3-dimensional q-deformed harmonic oscillator to the nuclear shell model
Raychev, P P; Lo-Iudice, N; Terziev, P A
1998-01-01
An analysis of the construction of a q-deformed version of the 3-dimensional harmonic oscillator, which is based on the application of q-deformed algebras, is presented. The results together with their applicability to the shell model are compared with the predictions of the modified harmonic oscillator.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Chiral potential renormalized in harmonic-oscillator space
Yang, C -J
2016-01-01
We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J-matrix method to reproduce the nucleon-nucleon (NN) scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy $T_{lab}=100$ MeV with number of HO basis $n_{max}$ as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. Our work serves as the input to perform ab-initio calculations.
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
Amitava Choudhuri; Subrata Ghosh; B Talukdar
2008-04-01
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the variational or Noether symmetries of the damped harmonic oscillator representing it by an explicitly time-dependent Lagrangian and found that a five-parameter group of transformations leaves the action integral invariant. Amongst the associated conserved quantities only two are found to be functionally independent. These two conserved quantities determine the solution of the problem and correspond to a two-parameter Abelian subgroup.
Geometric Models of the Quantum Relativistic Rotating Oscillator
Cotaescu, I I
1997-01-01
A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual isotropic harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is different. As in the case of the (1+1) models, these will have even countable energy spectra or mixed ones, with a finite discrete sequence and a continuous part. In addition, all these spectra, except that of the pure anti-de Sitter model, will have a fine-structure, given by a rotator-like term.
Entanglement dynamics of quantum oscillators nonlinearly coupled to thermal environments
Voje, Aurora; Croy, Alexander; Isacsson, Andreas
2015-07-01
We study the asymptotic entanglement of two quantum harmonic oscillators nonlinearly coupled to an environment. Coupling to independent baths and a common bath are investigated. Numerical results obtained using the Wangsness-Bloch-Redfield method are supplemented by analytical results in the rotating wave approximation. The asymptotic negativity as function of temperature, initial squeezing, and coupling strength, is compared to results for systems with linear system-reservoir coupling. We find that, due to the parity-conserving nature of the coupling, the asymptotic entanglement is considerably more robust than for the linearly damped cases. In contrast to linearly damped systems, the asymptotic behavior of entanglement is similar for the two bath configurations in the nonlinearly damped case. This is due to the two-phonon system-bath exchange causing a suppression of information exchange between the oscillators via the bath in the common-bath configuration at low temperatures.
Quantum Statistics of a Forced Oscillator with a Time-Dependent Driving Force
Institute of Scientific and Technical Information of China (English)
刘文森
2003-01-01
Quantum statistics of a forced harmonic oscillator acted upon by a time-dependent external force are derived using the Wilcox trick and the time-dependent inhomogeneous Bogoliubov transformation formalism.The internal energy,fluctuation of the particle-number average and entropy of this nonequilibrium system are presented explicitly.
Entangled Harmonic Oscillators and Space-time Entanglement
Baskal, Sibel; Noz, Marilyn E
2016-01-01
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of O(3,2) de Sitter group containing two O(3,1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of...
Spectral properties of a confined nonlinear quantum oscillator in one and three dimensions
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel; Gordon, Christopher R. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-04-15
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.
Decoherence and thermalization dynamics of a quantum oscillator
Dodonov, V V; De Souza-Silva, A L
2000-01-01
We introduce the quantitative measures characterizing the rates of decoherence and thermalization of quantum systems. We study the time evolution of these measures in the case of a quantum harmonic oscillator whose relaxation is described in the framework of the standard master equation, for various initial states (coherent, `cat', squeezed and number). We establish the conditions under which the true decoherence measure can be approximated by the linear entropy $1-{Tr}\\hat\\rho^2$. We show that at low temperatures and for highly excited initial states the decoherence process consists of three distinct stages with quite different time scales. In particular, the `cat' states preserve 50% of the initial coherence for a long time interval which increases logarithmically with increase of the initial energy.
Purity and decoherence in the theory of a damped harmonic oscillator
Isar, A.; Sandulescu, A.; Scheid, W.
1999-12-01
For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude, and weak coupling cases, and the Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with variances that are constant in time. For pure states, generalized nonlinear Schrödinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the particular models considered, expressions for the rate of entropy production are written, and it is shown that state which preserve their purity in time are also states which minimize entropy production and, therefore, are the most stable state under evolution in the presence of the environment, and play an important role in the description of decoherence phenomenon.
Novel Approach for Solving the Equation of Motion of a Simple Harmonic Oscillator. Classroom Notes
Gauthier, N.
2004-01-01
An elementary method, based on the use of complex variables, is proposed for solving the equation of motion of a simple harmonic oscillator. The method is first applied to the equation of motion for an undamped oscillator and it is then extended to the more important case of a damped oscillator. It is finally shown that the method can readily be…
Searching for robust quantum memories in many coupled oscillators
Energy Technology Data Exchange (ETDEWEB)
Bosco de Magalhaes, A.R., E-mail: arthur.magalhaes@pq.cnpq.br [Departamento de Fisica e Matematica, Centro Federal de Educacao Tecnologica de Minas Gerais, 30510-000, Belo Horizonte, MG (Brazil)
2011-11-07
The relation between microscopic symmetries in the system-environment interaction and the emergence of robust states is studied for many linearly coupled harmonic oscillators. Different types of symmetry, which are introduced into the model as terms in the coupling constants between each system's oscillator and a common reservoir, lead to distinct robust modes. Since these modes are partially or completely immune to the symmetric part of the environmental noise, they are good candidates for building quantum memories. A comparison of the model investigated here, with bilinear system-reservoir coupling, and a model where such coupling presents an exponential dependence on the variables of interest is performed. -- Highlights: → Macroscopic symmetries may lead to microscopic ones in system-environment coupling. → Robust modes related to these symmetries are found for N coupled oscillators. → They can be used to enhance the lifetime of quantum memories. → They can be built in cavity modes in photonic-band-gap material or trapped ions.
Generalized Harmonic Oscillator and the Schr(o)dinger Equation with Position-Dependent Mass
Institute of Scientific and Technical Information of China (English)
JU Guo-Xing; CAI Chang-Ying; REN Zhong-Zhou
2009-01-01
We study the generalized harmonic oscillator that has both the position-dependent mass and the potential depending on the form of mass function in a more general framework. The explicit expressions of the eigenvalue and eigenfunction for such a system are given, they have the same forms as those for the usual harmonic oscillator with constant mass. The coherent state and its properties for the system with PDM are also discussed. We give the corresponding effective potentials for several mass functions, the systems with such potentials are isospectral to the usual harmonic oscillator.
Electronically coarse-grained molecular dynamics using quantum Drude oscillators
Jones, A. P.; Crain, J.; Cipcigan, F. S.; Sokhan, V. P.; Modani, M.; Martyna, G. J.
2013-12-01
Standard molecular dynamics (MD) simulations generally make use of a basic description of intermolecular forces which consists of fixed, pairwise, atom-centred Coulomb, van der Waals and short-range repulsive terms. Important interactions such as many-body polarisation and many-body dispersion which are sensitive to changes in the environment are usually neglected, and their effects treated effectively within mean-field approximations to reproduce a single thermodynamic state point or physical environment. This leads to difficulties in modelling the complex interfaces of interest today where the behaviour may be quite different from the regime of parameterisation. Here, we describe the construction and properties of a Gaussian coarse-grained electronic structure, which naturally generates many-body polarisation and dispersion interactions. The electronic structure arises from a fully quantum mechanical treatment of a set of distributed quantum Drude oscillators (QDOs), harmonic atoms which interact with each other and other moieties via electrostatic (Coulomb) interactions; this coarse-grained approach is capable of describing many-body polarisation and dispersion but not short-range interactions which must be parametrised. We describe how on-the-fly forces due to this exchange-free Gaussian model may be generated with linear scale in the number of atoms in the system using an adiabatic path integral molecular dynamics for quantum Drude oscillators technique (APIMD-QDO). We demonstrate the applicability of the QDO approach to realistic systems via a study of the liquid-vapour interface of water.
Directory of Open Access Journals (Sweden)
Gilles Regniers
2009-11-01
Full Text Available In a system of coupled harmonic oscillators, the interaction can be represented by a real, symmetric and positive definite interaction matrix. The quantization of a Hamiltonian describing such a system has been done in the canonical case. In this paper, we take a more general approach and look at the system as a Wigner quantum system. Hereby, one does not assume the canonical commutation relations, but instead one just requires the compatibility between the Hamilton and Heisenberg equations. Solutions of this problem are related to the Lie superalgebras gl(1|n and osp(1|2n. We determine the spectrum of the considered Hamiltonian in specific representations of these Lie superalgebras and discuss the results in detail. We also make the connection with the well-known canonical case.
Harmonic and Dirac oscillators in a (2+1)-dimensional noncommutative space
Vega, F
2013-01-01
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible representation. The Hilbert space gets the structure of a direct product with the representation space as a factor, where there exist operators which realize the algebra of Lorentz transformations. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters, ?nding no constraints between coordinates and momenta noncom- mutativity parameters. Since the representation space of the unitary irreducible representations SL(2;R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension. PACS: 03.65.-w; 11.30.Cp; 02.40.Gh
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)
Neutrino oscillations: Quantum mechanics vs. quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Akhmedov, Evgeny Kh.; Kopp, Joachim
2010-01-01
A consistent description of neutrino oscillations requires either the quantum-mechanical (QM) wave packet approach or a quantum field theoretic (QFT) treatment. We compare these two approaches to neutrino oscillations and discuss the correspondence between them. In particular, we derive expressions for the QM neutrino wave packets from QFT and relate the free parameters of the QM framework, in particular the effective momentum uncertainty of the neutrino state, to the more fundamental parameters of the QFT approach. We include in our discussion the possibilities that some of the neutrino's interaction partners are not detected, that the neutrino is produced in the decay of an unstable parent particle, and that the overlap of the wave packets of the particles involved in the neutrino production (or detection) process is not maximal. Finally, we demonstrate how the properly normalized oscillation probabilities can be obtained in the QFT framework without an ad hoc normalization procedure employed in the QM approach.
Linear Harmonic Oscillator and Uniform Circular Motion%线性谐振子与匀速圆周运动
Institute of Scientific and Technical Information of China (English)
岳小萍; 秦鑫
2012-01-01
This article discusses the relationship between uniform circular motion and harmonic vibration of particle by classical mechanics method. The expressions of displacement, velocity and acceleration of linear harmonic oscillator are given, and phase differences among the three are explained by causality and Newton’s second law of motion. This article obtains linear harmonic oscillator force constant k = Gm m / r in-3 1 2 gravitational field, and discusses its physical significance, corrects the mistake of energy of harmonic oscillator is invariably positive for a long time. Electric linear harmonic oscillator concept is introduced. Method of discussing electric linear harmonic oscilators of elliptic orbit and valence electron in different orbital are provided. The method of converting linear harmonic oscillator of real space to quantum mechanics is introduced.% 用经典力学的方法讨论了质点匀速圆周运动与谐振动的关系问题，给出了线性谐振子位移、速度、加速度表达式，用因果律和牛顿第二运动定律，说明了三者之间的位相差关系；得到了万有引力场中二质点系统线性谐振子力常量k = Gm m / r 的结果，讨论了其物理意义，纠正了长期以来认为谐振子能量总是-312大于零的错误认识。引入了线性电谐振子概念；给出了讨论椭圆轨道电线性谐振子、不同轨道上价电子线性电谐振子的方法；介绍了实空间电线性谐振子转化为量子力学线性谐振子的方法
Anomalous diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise
Viñales, A. D.; Wang, K. G.; Despósito, M. A.
2009-07-01
The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using the Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions and its derivatives from a generalized Langevin equation. Our results show that the oscillator displays an anomalous diffusive behavior. In the strictly asymptotic limit, the dynamics of the harmonic oscillator corresponds to an oscillator driven by a noise with a pure power-law autocorrelation function. However, at short and intermediate times the dynamics has qualitative difference due to the presence of the characteristic time of the noise.
Large- quantum chromodynamics and harmonic sums
Indian Academy of Sciences (India)
Eduardo De Rafael
2012-06-01
In the large- limit of QCD, two-point functions of local operators become harmonic sums. I review some properties which follow from this fact and which are relevant for phenomenological applications. This has led us to consider a class of analytic number theory functions as toy models of large- QCD which also is discussed.
On the limiting behavior of a harmonic oscillator with random external disturbance
Directory of Open Access Journals (Sweden)
G. L. Kulinich
1995-01-01
Full Text Available This paper deals with the limiting behavior of a harmonic oscillator under the external random disturbance that is a process of the white noise type. Influence of noises is investigated in resonance and non-resonance cases.
Propagator for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity
Institute of Scientific and Technical Information of China (English)
HUANG Bo-Wen; GU Zhi-Yu; QIAN Shang-Wu
2003-01-01
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant.
The calculating formula for radial matrix elements of a relativistic harmonic oscillator
Institute of Scientific and Technical Information of China (English)
强稳朝
2003-01-01
A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial matrix elements for a relativistic harmonic oscillator are given.
Transformation between harmonic-oscillator wave functions in different coordinate bases
Energy Technology Data Exchange (ETDEWEB)
Davies, K.T.R.; Krieger, S.J.
1981-10-01
Coefficients are derived for transformations between harmonic oscillator wave functions in different coordinate representations. Such coefficients have been found especially useful in performing static Hartree-Fock calculations for nuclei of widely varying shapes.
Quantum Gravity signals in neutrino oscillations
Sprenger, Martin; Bleicher, Marcus
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.
Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator
Indian Academy of Sciences (India)
PETER A ROSE; ANDREW C McCLUNG; TYLER E KEATING; ADAM T C STEEGE; ERIC S EGGE; ARJENDU K PATTANAYAK
2016-08-01
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 all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates $|n\\ rangle$, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state $n*$ with maximal quantum-classical distance; the value $n*$ decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.
A Fulling-Kuchment theorem for the 1D harmonic oscillator
Guillemin, Victor
2011-01-01
We prove that there exists a pair of "non-isospectral" 1D semiclassical Schr\\"odinger operators whose spectra agree modulo h^\\infty. In particular, all their semiclassical trace invariants are the same. Our proof is based on an idea of Fulling-Kuchment and Hadamard's variational formula applied to suitable perturbations of the harmonic oscillator. Keywords: Inverse spectral problems, semiclassical Schr\\"odinger operators, trace invariants, Hadamard's variational formula, harmonic oscillator, Penrose mushroom, Sturm-Liouville theory.
Quantum states with continuous spectrum for a general time-dependent oscillator
Indian Academy of Sciences (India)
Jeong-Ryeol Choi
2005-08-01
We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator: $\\hat{I'} = \\hat{p}^{2}/2 + ^{2}\\hat{q}^{2}/2$. The fact that 2 of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, where 2 > 0, 2 < 0, and 2 = 0. The eigenstates of the system are discrete for 2 > 0. On the other hand, for 2 ≤ 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function for 2 < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.
Second-harmonic scanning optical microscopy of semiconductor quantum dots
DEFF Research Database (Denmark)
Vohnsen, B.; Bozhevolnyi, S.I.; Pedersen, K.;
2001-01-01
Second-harmonic (SH) optical imaging of self-assembled InAlGaAs quantum dots (QD's) grown on a GaAs(0 0 1) substrate has been accomplished at room temperature by use of respectively a scanning far-field optical microscope in reflection mode and a scanning near-field optical microscope...
Energy Technology Data Exchange (ETDEWEB)
Thantu, Napoleon; McMorrow, D.; Melinger, J. S.; Kleiman, V.; Lotshaw, W. T.
2001-07-01
The apparently-multicomponent subpicosecond intermolecular dynamics of carbon disulfide liquid are addressed in a unified manner in terms of an inhomogeneously broadened quantum mechanical harmonic oscillator model for a single vibrational coordinate. For an inhomogeneously broadened (Gaussian) distribution of oscillators, the model predicts naturally the bimodal character of the subpicosecond intermolecular dynamics of carbon disulfide liquid, and also the spectral evolution effects (spectral narrowing and saturation) that are observed for solutions of carbon disulfide in weakly interacting alkane solvents. The unique dynamical signature of these low-frequency vibrational coordinates is determined largely by the physical constraints on the coordinates (near equality of oscillator frequency, dephasing frequency, and inhomogeneous bandwidth), such that constructive and destructive interference effects play a dominant role in shaping the experimental observable.
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.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-01
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.
Quantum harmonic Brownian motion in a general environment: A modified phase-space approach
Energy Technology Data Exchange (ETDEWEB)
Yeh, L. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley Lab., CA (United States)
1993-06-23
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.
Bonatsos, Dennis; Lenis, D; Raychev, P P; Roussev, R P; Terziev, P A
2000-01-01
Magic numbers predicted by a 3-dimensional q-deformed harmonic oscillator with Uq(3)>SOq(3) symmetry are compared to experimental data for atomic clusters of alkali metals (Li, Na, K, Rb, Cs), noble metals (Cu, Ag, Au), divalent metals (Zn, Cd), and trivalent metals (Al, In), as well as to theoretical predictions of jellium models, Woods-Saxon and wine bottle potentials, and to the classification scheme using the 3n+l pseudo quantum number. In alkali metal clusters and noble metal clusters the 3-dimensional q-deformed harmonic oscillator correctly predicts all experimentally observed magic numbers up to 1500 (which is the expected limit of validity for theories based on the filling of electronic shells), while in addition it gives satisfactory results for the magic numbers of clusters of divalent metals and trivalent metals, thus indicating that Uq(3), which is a nonlinear extension of the U(3) symmetry of the spherical (3-dimensional isotropic) harmonic oscillator, is a good candidate for being the symmetry ...
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 correlations in terms of neutrino oscillation probabilities
Ashutosh Kumar Alok; Subhashish Banerjee; Uma Sankar, S.(Indian Institute of Technology Bombay, Mumbai, 400076, India)
2016-01-01
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 t...
Degenerate parametric oscillation in quantum membrane optomechanics
Benito, Mónica; Sánchez Muñoz, Carlos; Navarrete-Benlloch, Carlos
2016-02-01
The promise of innovative applications has triggered the development of many modern technologies capable of exploiting quantum effects. But in addition to future applications, such quantum technologies have already provided us with the possibility of accessing quantum-mechanical scenarios that seemed unreachable just a few decades ago. With this spirit, in this work we show that modern optomechanical setups are mature enough to implement one of the most elusive models in the field of open system dynamics: degenerate parametric oscillation. Introduced in the eighties and motivated by its alleged implementability in nonlinear optical resonators, it rapidly became a paradigm for the study of dissipative phase transitions whose corresponding spontaneously broken symmetry is discrete. However, it was found that the intrinsic multimode nature of optical cavities makes it impossible to experimentally study the model all the way through its phase transition. In contrast, here we show that this long-awaited model can be implemented in the motion of a mechanical object dispersively coupled to the light contained in a cavity, when the latter is properly driven with multichromatic laser light. We focus on membranes as the mechanical element, showing that the main signatures of the degenerate parametric oscillation model can be studied in state-of-the-art setups, thus opening the possibility of analyzing spontaneous symmetry breaking and enhanced metrology in one of the cleanest dissipative phase transitions. In addition, the ideas put forward in this work would allow for the dissipative preparation of squeezed mechanical states.
Double-Paddle Oscillators as Probes of Quantum Turbulence in the Zero Temperature Limit
Schmoranzer, David; Jackson, Martin; Zemma, Elisa; Luzuriaga, Javier
2016-11-01
We present a technical report on our tests of a double-paddle oscillator as a detector of quantum turbulence in superfluid 4 He at low temperatures ranging from 20 to 1100 mK. The device, known to operate well in the two-fluid regime (Zemma and Luzuriaga in J Low Temp Phys 166:171-181, 2012), is also capable of detecting quantum turbulence in the zero temperature limit. The oscillator demonstrated Lorentzian responses with quality factors of order 10^5 in vacuum, and displayed negative-Duffing resonances in liquid, even at moderate drives. In superfluid He-II at low temperatures, its sensitivity was adversely affected by acoustic damping at higher harmonics. While it successfully created and detected the quantum turbulence, its overall performance does not compare favourably with other oscillators such as tuning forks.
Teh, Mei-Hui; LeBohec, Stephan
2016-01-01
This article is the first in a series of two presenting the scale relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. In this first paper, we present the definition of a complex "scale-covariant time-differential operator" and show that mechanics of non-differentiable paths is implemented in the same way as classical mechanics but with the replacement of the time derivative and velocity with the time-differential operator and associated complex velocity. With this, the generalized form of Newton's fundamental relation of dynamics is shown to take the form of a Langevin equation in the case of stationary motion characterized by a null average classical velocity. The numerical integration of the Langevin equation in the case of a harmonic oscillator reveals the same statistics as the stationary solutions of the Schrodinger equation for the same problem. This motivates the second paper which makes the relation to quantum mechanics explicit by discussing the axioms o...
Bohá\\{v}cik, J; August\\'\\{i}n, P
2013-01-01
We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.
Quantum Dynamics of Mesoscopic Driven Duffing Oscillators
Guo, Lingzhen; Li, Xin-Qi
2009-01-01
We investigate the nonlinear dynamics of a mesoscopic driven Duffing oscillator in a quantum regime. In terms of Wigner function, we identify the nature of state near the bifurcation point, and analyze the transient process which reveals two distinct stages of quenching and escape. The rate process in the escape stage allows us to extract the transition rate, which displays perfect scaling behavior with the driving distance to the bifurcation point. We numerically determine the scaling exponent, compare it with existing analytic result, and suggest its possible observation.
Quantum correlation in degenerate optical parametric oscillators with mutual injections
Takata, Kenta
2015-01-01
We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections are simulated, and their quantum states are investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\\hat{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, and the entanglement between the intracavity subharmonic fields. When with a small loss of the injection path, each oscillator around the phase transition point forms macroscopic superposition for a small pump noise. It suggests that the low-loss injection path works as a sq...
Construction of exact Ermakov-Pinney solutions and time-dependent quantum oscillators
Kim, Sang Pyo; Kim, Won
2016-11-01
The harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schrödinger equation, which are determined by any two independent solutions to the classical equation of motion. Ermakov and Pinney have shown that a general solution to the time-dependent oscillator with an inverse cubic term can be expressed in terms of two independent solutions to the time-dependent oscillator. We explore the connection between linear quantum invariants and the Ermakov-Pinney solution for the time-dependent harmonic oscillator. We advance a novel method to construct Ermakov-Pinney solutions to a class of time-dependent oscillators and the wave functions for the time-dependent Schrödinger equation. We further show that the first and the second Pöschl-Teller potentials belong to a special class of exact time-dependent oscillators. A perturbation method is proposed for any slowly-varying time-dependent frequency.
Double Fourier Harmonic Balance Method for Nonlinear Oscillators by Means of Bessel Series
2014-10-16
Duffing oscillator . As an example of the results, the predicted period of a simple pendulum swinging between −90° and +90° is found to be only 0.4% larger...Eq. (42). 4.5 The Duffing oscillator with zero linear term For an anharmonic oscillator having restoring force f(x) = αx3, define ω0 = A √ α. Using...Double Fourier harmonic balance method for nonlinear oscillators by means of Bessel series T.C. Lipscombe∗1 and C.E. Mungan†2 1Catholic University of
Institute of Scientific and Technical Information of China (English)
ZHANG Li; XIE Hong-Jing
2003-01-01
Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic Q W have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic Q W systems.
Institute of Scientific and Technical Information of China (English)
ZHANGLi; XIEHong-Jing
2003-01-01
Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.
Bloch-Like Oscillations in Finite Quantum Structures
DEFF Research Database (Denmark)
Duggen, Lars; Willatzen, Morten; Lassen, Benny;
Inspired by several attempts to generate Bloch-like oscillations in different fields of physics [1,2], we examine a multitude of oscillator systems and interactions that lead to Bloch oscillations in finite quantum structures. A general requirement is the existence of a common period in the time...... of individual quantum wells and changing the coupling strength as a function of position. It is, furthermore, demonstrated that the application of a magnetic field to a structure of quantum wells may lead to the observation of Bloch oscillations (similar to Bloch oscillations stemming from the Stark effect......) and derive rather general mathematical relations between quantum systems that allow the existence of Bloch oscillations. References: [1]: G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, and R. Osellame, Nature Communications 4, 1555 (2013) [2]: H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez...
Directory of Open Access Journals (Sweden)
Yilun Shang
2012-07-01
Full Text Available In this paper, we investigate the leader-follower synchronization ofcoupled second-order linear harmonic oscillators with the presence ofrandom noises and time delays. The interaction topology is modeledby a weighted directed graph and the weights are perturbed by whitenoise. On the basis of stability theory of stochastic differential delayequations, algebraic graph theory and matrix theory, we show that thecoupled harmonic oscillators can be synchronized almost surely withrandom perturbation and time delays. Numerical examples are presentedto illustrate our theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Martinez, D [Universidad Autonoma de la Ciudad de Mexico, Plantel Cuautepec, Av. La Corona 320, Col. Loma la Palma, Delegacion Gustavo A. Madero, 07160, Mexico DF (Mexico); Flores-Urbina, J C; Mota, R D [Unidad Profesional Interdisciplinaria de Ingenieria y Tecnologias Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, Delegacion Gustavo A. Madero, 07340 Mexico DF (Mexico); Granados, V D [Escuela Superior de Fisica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)], E-mail: dmartinezs77@yahoo.com.mx
2010-04-02
We apply the Schroedinger factorization to construct the ladder operators for the hydrogen atom, Mie-type potential, harmonic oscillator and pseudo-harmonic oscillator in arbitrary dimensions. By generalizing these operators we show that the dynamical algebra for these problems is the su(1, 1) Lie algebra.
Optimal analysis on the performance of an irreversible harmonic quantum Brayton refrigeration cycle.
Lin, Bihong; Chen, Jincan
2003-11-01
An irreversible model of a quantum refrigeration cycle working with many noninteracting harmonic oscillators is established. The refrigeration cycle consists of two adiabatic and two constant-frequency processes. The general performance characteristics of the cycle are investigated, based on the quantum master equation and the semigroup approach. The expressions for several important performance parameters such as the coefficient of performance, cooling rate, power input, and rate of entropy production are derived. By using numerical solutions, the cooling rate of the refrigeration cycle subject to finite cycle duration is optimized. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal region of the coefficient of performance and the optimal ranges of temperatures of the working substance and times spent on the two constant-frequency processes are determined. Moreover, the optimal performance of the cycle in the high-temperature limit is compared with that of a classical Brayton refrigerator working with an ideal gas. The results obtained here show that in the high-temperature limit a harmonic quantum Brayton cycle may be equivalent to a classical Brayton cycle.
Institute of Scientific and Technical Information of China (English)
刘宇峰; 曾谨言
1997-01-01
The factorization of the radial Schrodinger equation of n-dimensional (n≥2) hydrogen atoms and isotropic harmonic oscillators was investigated and four kinds of raising and lowering operators were derived.The relation between n -dimensional (n≥2) and one-dimensional hydrogen atoms and harmonic oscillators was discussed.
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens;
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...
Exact solutions of N-dimensional harmonic oscillator via Laplace transformation
Institute of Scientific and Technical Information of China (English)
Chen Gang
2005-01-01
The N-dimensional Schrodinger equation for the harmonic oscillator is reduced to a first-order differential equation in terms of the Laplace transformation and the exact bound state solutions are derived. It is shown that this method of solving Schrodinger equation may serve as a substitute for the standard functional, analytical approach also in lower dimensions.
su(2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator
Martínez, D.; Avendaño, C. G.
2014-04-01
We evaluate the Feynman propagator for the harmonic oscillator in one dimension. Considering the ladder operators for the Hamiltonian of this system, we construct a set of operators which satisfy the su(2) Lie algebra to obtain Mehler’s formula.
Convergence for Fourier Series Solutions of the Forced Harmonic Oscillator II
Fay, Temple H.
2002-01-01
This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…
Generalized Uncertainty Principle Corrections to the Simple Harmonic Oscillator in Phase Space
Das, Saurya; Walton, Mark A
2016-01-01
We compute Wigner functions for the harmonic oscillator including corrections from generalized uncertainty principles (GUPs), and study the corresponding marginal probability densities and other properties. We show that the GUP corrections to the Wigner functions can be significant, and comment on their potential measurability in the laboratory.
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...
Density Matrix and Squeezed Vacuum State for General Coupling Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
SONG Tong-Qiang
2003-01-01
By taking a unitary transformation approach, we study two harmonic oscillators with both kinetic coupling and coordinate coupling terms, and derive the density matrix of the system. The results show that the ground state of the system is a rotated two single-mode squeezed state.
Exact Solutions of Two Coupled Harmonic Oscillators Related to the Sp(4, R) Lie Algebra
Institute of Scientific and Technical Information of China (English)
PAN Feng; DAI LianRong
2001-01-01
Exact solutions of the eigenvalue problem of two coupled harmonic oscillators related to the Sp(4, R) Lie algebra are derived by using an algebraic method. It is found that the energy spectrum of the system is determined by one-boson excitation energies built on a vector coherent state of Sp(4, R) U(2).``
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
Directory of Open Access Journals (Sweden)
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Equilibrium and stationary nonequilibrium states in a chain of colliding harmonic oscillators
Sano
2000-02-01
Equilibrium and nonequilibrium properties of a chain of colliding harmonic oscillators (ding-dong model) are investigated. Our chain is modeled as harmonically bounded particles that can only interact with neighboring particles by hard-core interaction. Between the collisions, particles are just independent harmonic oscillators. We are especially interested in the stationary nonequilibrium state of the ding-dong model coupled with two stochastic heat reservoirs (not thermostated) at the ends, whose temperature is different. We check the Gallavotti-Cohen fluctuation theorem [G. Gallavoti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995)] and also the Evans-Searles identity [D. Evans and D. Searles, Phys. Rev. E. 50, 1994 (1994)] numerically. It is verified that the former theorem is satisfied for this system, although the system is not a thermostated system.
Simulation of neutrino oscillations using discrete-time quantum walk
Mallick, Arindam; Chandrashekar, C M
2016-01-01
Neutrino oscillation is a well-known phenomenon observed in high energy physics. Here starting from a one-spatial dimensional discrete-time quantum walk we present a method to simulate neutrino oscillation. We present the set of walk parameters with which we can obtain the same oscillation probability profile obtained in both, long range and short range neutrino experiment. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental setup with access to control a single six-level system, a multiparticle three-qubits or a qubit-qutrit system.
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.
Quantum correlations in terms of neutrino oscillation probabilities
Alok, Ashutosh Kumar; Banerjee, Subhashish; Uma Sankar, S.
2016-08-01
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.
Stepšys, A.; Mickevicius, S.; Germanas, D.; Kalinauskas, R. K.
2014-11-01
This new version of the HOTB program for calculation of the three and four particle harmonic oscillator transformation brackets provides some enhancements and corrections to the earlier version (Germanas et al., 2010) [1]. In particular, new version allows calculations of harmonic oscillator transformation brackets be performed in parallel using MPI parallel communication standard. Moreover, higher precision of intermediate calculations using GNU Quadruple Precision and arbitrary precision library FMLib [2] is done. A package of Fortran code is presented. Calculation time of large matrices can be significantly reduced using effective parallel code. Use of Higher Precision methods in intermediate calculations increases the stability of algorithms and extends the validity of used algorithms for larger input values. Catalogue identifier: AEFQ_v4_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFQ_v4_0.html Program obtainable from: CPC Program Library, Queen’s University of Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 Number of lines in programs, including test data, etc.: 1711 Number of bytes in distributed programs, including test data, etc.: 11667 Distribution format: tar.gz Program language used: FORTRAN 90 with MPI extensions for parallelism Computer: Any computer with FORTRAN 90 compiler Operating system: Windows, Linux, FreeBSD, True64 Unix Has the code been vectorized of parallelized?: Yes, parallelism using MPI extensions. Number of CPUs used: up to 999 RAM(per CPU core): Depending on allocated binomial and trinomial matrices and use of precision; at least 500 MB Catalogue identifier of previous version: AEFQ_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181, Issue 2, (2010) 420-425 Does the new version supersede the previous version? Yes Nature of problem: Calculation of matrices of three-particle harmonic oscillator brackets (3HOB) and four-particle harmonic oscillator brackets (4HOB) in a more
Ehlers, E. F.
1974-01-01
A finite difference method for the solution of the transonic flow about a harmonically oscillating wing is presented. The partial differential equation for the unsteady transonic flow was linearized by dividing the flow into separate steady and unsteady perturbation velocity potentials and by assuming small amplitudes of harmonic oscillation. The resulting linear differential equation is of mixed type, being elliptic or hyperbolic whereever the steady flow equation is elliptic or hyperbolic. Central differences were used for all derivatives except at supersonic points where backward differencing was used for the streamwise direction. Detailed formulas and procedures are described in sufficient detail for programming on high speed computers. To test the method, the problem of the oscillating flap on a NACA 64A006 airfoil was programmed. The numerical procedure was found to be stable and convergent even in regions of local supersonic flow with shocks.
Institute of Scientific and Technical Information of China (English)
Chang-shui FENG; Wei-qiu ZHU
2009-01-01
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged Ito stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov (FPK) equation associated with the averaged Ito equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus-trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
Energy levels of. lambda. x sup 2k anharmonic oscillators using the quantum normal form
Energy Technology Data Exchange (ETDEWEB)
Brajamani, S.; Mazumdar, P.S. (Manipur Univ., (India)); Chowdhury, S.K.; Sur, S. (Indian Association for the Cultivation of Science, West Bengal (India))
1991-04-01
In recent years there has been a large and important literature on the methods for studying a well-known class of single-well quantum anharmonic oscillators. These one-body Schroedinger problems have played a particularly important role in recent years as model bosonic field theories which contain only one mode. This mode is generated by the usual harmonic oscillator creation operator {alpha}. In this respect the anharmonic oscillators may be considered as the (0+1)-dimensional counterparts of more realistic quantum field theories in the physical world of (3+1)-dimensionality. The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the Hamiltonian H = {minus}d{sup 2}/dx{sup 2}+x{sup 2}+{lambda}x{sup 2k} (k = 3,4,{hor ellipsis}) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels.
Kondo Breakdown and Quantum Oscillations in SmB_{6}.
Erten, Onur; Ghaemi, Pouyan; Coleman, Piers
2016-01-29
Recent quantum oscillation experiments on SmB_{6} pose a paradox, for while the angular dependence of the oscillation frequencies suggest a 3D bulk Fermi surface, SmB_{6} remains robustly insulating to very high magnetic fields. Moreover, a sudden low temperature upturn in the amplitude of the oscillations raises the possibility of quantum criticality. Here we discuss recently proposed mechanisms for this effect, contrasting bulk and surface scenarios. We argue that topological surface states permit us to reconcile the various data with bulk transport and spectroscopy measurements, interpreting the low temperature upturn in the quantum oscillation amplitudes as a result of surface Kondo breakdown and the high frequency oscillations as large topologically protected orbits around the X point. We discuss various predictions that can be used to test this theory.
Energy Technology Data Exchange (ETDEWEB)
Atakishiyev, N.M. [Instituto de Matematicas. Universidad Nacional Autonoma de Mexico. Cuernavaca, Morelos (Mexico); Jafarov, E.I.; Nagiyev, S.M. [Institute of Physics, Azerbaijan Academy of Sciences. Baku, Azerbaijan (Azerbaijan); Wolf, K.B. [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas. Universidad Nacional Autonoma de Mexico. Cuernavaca, Morelos (Mexico)
1998-10-01
Meixner oscillators have a ground state and an energy spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a difference operator. Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators. By the Sommerfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and their continuous weight function. We construct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,R). The reproducing kernel for the wavefunctions of these models is also found. (Author)
Thermodynamic constraints on the amplitude of quantum oscillations
Shekhter, Arkady; Modic, K. A.; McDonald, R. D.; Ramshaw, B. J.
2017-03-01
Magneto-quantum oscillation experiments in high-temperature superconductors show a strong thermally induced suppression of the oscillation amplitude approaching the critical dopings [B. J. Ramshaw et al., Science 348, 317 (2014), 10.1126/science.aaa4990; H. Shishido et al., Phys. Rev. Lett. 104, 057008 (2010), 10.1103/PhysRevLett.104.057008; P. Walmsley et al., Phys. Rev. Lett. 110, 257002 (2013), 10.1103/PhysRevLett.110.257002]—in support of a quantum-critical origin of their phase diagrams. We suggest that, in addition to a thermodynamic mass enhancement, these experiments may directly indicate the increasing role of quantum fluctuations that suppress the quantum oscillation amplitude through inelastic scattering. We show that the traditional theoretical approaches beyond Lifshitz-Kosevich to calculate the oscillation amplitude in correlated metals result in a contradiction with the third law of thermodynamics and suggest a way to rectify this problem.
Optomechanical entanglement of a macroscopic oscillator by quantum feedback
Wu, E.; Li, Fengzhi; Zhang, Xuefeng; Ma, Yonghong
2016-07-01
We propose a scheme to generate the case of macroscopic entanglement in the optomechanical system, which consist of Fabry-Perot cavity and a mechanical oscillator by applying a homodyne-mediated quantum feedback. We explore the effect of feedback on the entanglement in vacuum and coherent state, respectively. The results show that the introduction of quantum feedback can increase the entanglement effectively between the cavity mode and the oscillator mode.
Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators
Lörch, Niels; Amitai, Ehud; Nunnenkamp, Andreas; Bruder, Christoph
2016-08-01
We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.
Optimal Power and Efficiency of Quantum Thermoacoustic Micro-cycle Working in 1D Harmonic Trap
E, Qing; Wu, Feng; Yin, Yong; Liu, XiaoWei
2017-10-01
Thermoacoustic engines (including heat engines and refrigerators) are energy conversion devices without moving part. They have great potential in aviation, new energy utilization, power technology, refrigerating and cryogenics. The thermoacoustic parcels, which compose the working fluid of a thermoacoustic engine, oscillate within the sound channel with a temperature gradient. The thermodynamic foundation of a thermoacoustic engine is the thermoacoustic micro-cycle (TAMC). In this paper, the theory of quantum mechanics is applied to the study of the actual thermoacoustic micro-cycle for the first time. A quantum mechanics model of the TAMC working in a 1D harmonic trap, which is named as a quantum thermoacoustic micro-cycle (QTAMC), is established. The QTAMC is composed of two constant force processes connected by two straight line processes. Analytic expressions of the power output and the efficiency for QTAMC have been derived. The effects of the trap width and the temperature amplitude on the power output and the thermal efficiency have been discussed. Some optimal characteristic curves of power output versus efficiency are plotted, and then the optimization region of QTAMC is given in this paper. The results obtained here not only enrich the thermoacoustic theory but also expand the application of quantum thermodynamics.
An easy trick to a periodic solution of relativistic harmonic oscillator
Directory of Open Access Journals (Sweden)
Jafar Biazar
2014-04-01
Full Text Available In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.
Directory of Open Access Journals (Sweden)
Sameer M. Ikhdair
2014-10-01
Full Text Available The two-dimensional solution of the spinless Klein–Gordon (KG equation for scalar–vector harmonic oscillator potentials with and without the presence of constant perpendicular magnetic and Aharonov–Bohm (AB flux fields is studied within the asymptotic function analysis and Nikiforov–Uvarov (NU method. The exact energy eigenvalues and normalized wave functions are analytically obtained in terms of potential parameters, magnetic field strength, AB flux field and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL = 0 and AB flux field (ξ = 0 case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.
Dynamic quantum tunneling in mesoscopic driven Duffing oscillators.
Guo, Lingzhen; Zheng, Zhigang; Li, Xin-Qi; Yan, Yijing
2011-07-01
We investigate the dynamic quantum tunneling between two attractors of a mesoscopic driven Duffing oscillator. We find that, in addition to inducing a remarkable quantum shift of the bifurcation point, the mesoscopic nature also results in a perfect linear scaling behavior for the tunneling rate with the driving distance to the shifted bifurcation point.
Forced harmonic oscillations of the Euler-Bernoulli beam with resistance forces
Directory of Open Access Journals (Sweden)
Yuriy S. Krutiy
2015-12-01
Full Text Available The important issue in the oscillation theory is the study of resistance impact on oscillatory processes. Unlike the calculations of free oscillations, that reside in determination of natural frequencies and waveshapes and unlike the calculations of forced oscillations far away from resonance, that are performing without reference to friction, the oscillations researches in vicinity of resonance need accounting of friction forces. Special attention is paid to forced transverse fluctuations in beams as an important technical problem for engineering and building. Aim: The aim of the work is constructing of analytical solution of the problem of forced transverse vibrations of a straight rod with constant cross-section, which is under the influence of the harmonic load taking into account external and internal resistances. Materials and Methods: The internal resistance is taken into account using the corrected hypothesis of Kelvin-Voigt which reflects the empirically proven fact about the frequency-independent internal friction in the material. The external friction is also considered as frequency-independent. Results: An analytical solution is built for the differential equation of forced transverse oscillations of a straight rod with constant cross-section which is under the influence of the harmonic load taking into account external and internal resistances. As a result, analytically derived formulae are presented which describe the forced dynamic oscillations and the dynamic internal forces due to the harmonic load applied to the rod thus reducing the problem with any possible fixed ends to the search of unknown integration constants represented in a form of initial parameters.
Charged oscillator quantum state generation with Rydberg atoms
Stevenson, Robin; Hofferberth, Sebastian; Lesanovsky, Igor
2016-01-01
We explore the possibility of engineering quantum states of a charged mechanical oscillator by coupling it to a stream of atoms in superpositions of high-lying Rydberg states. Our scheme relies on the driving of a two-phonon resonance within the oscillator by coupling it to an atomic two-photon transition. This approach effectuates a controllable open system dynamics on the oscillator that permits the creation of squeezed and other non-classical states. We show that these features are robust to thermal noise arising from a coupling of the oscillator with the environment. The possibility to create non-trivial quantum states of mechanical systems, provided by the proposed setup, is central to applications such as sensing and metrology and moreover allows the exploration of fundamental questions concerning the boundary between classical and quantum mechanical descriptions of macroscopic objects.
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Midya, Bikashkali; Roychoudhury, Rajkumar
2011-01-01
The generalized Swanson Hamiltonian $H_{GS} = w (\\tilde{a}\\tilde{a}^\\dag+ 1/2) + \\alpha \\tilde{a}^2 + \\beta \\tilde{a}^{\\dag^2}$ with $\\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as $[\\tilde{a},\\tilde{a}^\\dag]=$ constant. However, the main objective of this paper is to show that though the commutator of $\\tilde{a}$ and $\\tilde{a}^\\dag$ is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. Reason for this anomaly is discussed in the frame work of position dependent mass models by choosing $A(x)$ as the inverse square root of the mass function.
Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions
Ferkous, N.; Boudjedaa, T.
2017-03-01
We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function techniques using both momentum and position space representations. The even and odd solutions of the problem are discussed. The corresponding limiting cases are recovered. For the harmonic oscillator with a point interaction in more than one dimension, divergent series appear. We use to remove this divergence an exponential regulator and we obtain a transcendental equation for the energy bound states. The results obtained here are consistent with other investigations using different methods. Supported by the Algerian Ministry of Higher Education and Scientific Research under the CNEPRU project No. D01720140001
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Directory of Open Access Journals (Sweden)
Md. Alal Hosen
2015-01-01
Full Text Available In the present paper, a complicated strongly nonlinear oscillator with cubic and harmonic restoring force, has been analysed and solved completely by harmonic balance method (HBM. Investigating analytically such kinds of oscillator is very difficult task and cumbersome. In this study, the offered technique gives desired results and to avoid numerical complexity. An excellent agreement was found between approximate and numerical solutions, which prove that HBM is very efficient and produces high accuracy results. It is remarkably important that, second-order approximate results are almost same with exact solutions. The advantage of this method is its simple procedure and applicable for many other oscillatory problems arising in science and engineering.
A Novel SIW-Based Planar W-Band GaAs Gunn Harmonic Oscillator
Liu, Yong; Tang, Xiao-Hong; Cao, Zhou
2010-10-01
Based on the substrate integrated waveguide (SIW) technology, a novel W-band low phase noise GaAs Gunn planar harmonic oscillator is developed in this paper. The technique of harmonic extraction from Gunn diodes and SIW resonant cavity structures are discussed in detail. Due to the high quality factor and planar structure of the SIW cavity resonator, the oscillator is characterized by some advantages such as low phase noise, small size, low cost and planar integration. The measured phase noise is -108.56 dBc/Hz at 1 MHz offset and the output power is more than 9 dBm at 94.78 GHz. A 300 MHz of linear tuning range with power fluctuation less than 1.5 dB is observed when the Gunn diode is biased from 4 to 5.3 V.
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.
Cooling a Harmonic Oscillator by Optomechanical Modification of Its Bath
Xu, Xunnong; Purdy, Thomas; Taylor, Jacob M.
2017-06-01
Optomechanical systems show tremendous promise for the high-sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce an additional damping channel to mechanical motion while keeping its thermal noise at the same level, and, as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of the temperature to the quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red-detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.
Pulsed high harmonic generation of light due to pumped Bloch oscillations in noninteracting metals
Freericks, J K; Kemper, A F; Devereaux, T P; 10.1088/0031-8949/2012/T151/014062
2012-01-01
We derive a simple theory for high-order harmonic generation due to pumping a noninteracting metal with a large amplitude oscillating electric field. The model assumes that the radiated light field arises from the acceleration of electrons due to the time-varying current generated by the pump, and also assumes that the system has a constant density of photoexcited carriers, hence it ignores the dipole excitation between bands (which would create carriers in semiconductors). We examine the circumstances under which odd harmonic frequencies would be expected to dominate the spectrum of radiated light, and we also apply the model to real materials like ZnO, for which high-order harmonic generation has already been demonstrated in experiments.
Fujita, Toshiyuki; Sasaki, Takahiko; Yoneyama, Naoki; Kobayashi, Norio
2004-04-01
We report on the low-frequency AC higher harmonic response measurements in the density wave state of the layered organic conductor α-(BEDT-TTF) 2KHg(SCN) 4. The non-linear conduction in the longitudinal magnetoresistance is detected as the enhancement of the higher harmonic response. The magnitude of the non-linearity oscillates in the high magnetic field with the same frequency of the Shubnikov-de Haas oscillations. The observation is suggestive of the presence of the successive field-induced transition of the density wave state synchronized with the quantum oscillation in high magnetic fields.
Energy Technology Data Exchange (ETDEWEB)
Fujita, Toshiyuki; Sasaki, Takahiko; Yoneyama, Naoki; Kobayashi, Norio
2004-04-30
We report on the low-frequency AC higher harmonic response measurements in the density wave state of the layered organic conductor {alpha}-(BEDT-TTF){sub 2}KHg(SCN){sub 4}. The non-linear conduction in the longitudinal magnetoresistance is detected as the enhancement of the higher harmonic response. The magnitude of the non-linearity oscillates in the high magnetic field with the same frequency of the Shubnikov-de Haas oscillations. The observation is suggestive of the presence of the successive field-induced transition of the density wave state synchronized with the quantum oscillation in high magnetic fields.
On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator
Figueiredo Camargo, R.; Capelas de Oliveira, E.; Vaz, J.
2009-12-01
The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.
Parallel-path biquad active-RC oscillator with enhanced harmonic rejection
Vosper, J. V.; Heima, M.; Cryan, R. A.
1995-04-01
A biquad active-RC oscillator is described and a linear analysis given which shows that harmonics injected within the feedback loop are multiplied by a factor which is inversely proportional to the effective open-loop Q-factor Q(sub 0). Experimental results show that distortion is low at high Q(sub 0) values even when saturated operation of the main gain-producing opamp is allowed.
Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))
1993-11-29
Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....
Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.
Li, Haifeng; Shao, Jiushu; Wang, Shikuan
2011-11-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.
Das, A; Das, A; Wotzasek, C
1995-01-01
We study a supersymmetric 2-dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2\\vert1) formulate it on the superspace, and discuss its physical spectrum.
Quantum, classical and semiclassical analyses of photon statistics in harmonic generation
Bajer, J; Bajer, Jiri; Miranowicz, Adam
2001-01-01
In this review, we compare different descriptions of photon-number statistics in harmonic generation processes within quantum, classical and semiclassical approaches. First, we study the exact quantum evolution of the harmonic generation by applying numerical methods including those of Hamiltonian diagonalization and global characteristics. We show explicitly that the harmonic generations can indeed serve as a source of nonclassical light. Then, we demonstrate that the quasi-stationary sub-Poissonian light can be generated in these quantum processes under conditions corresponding to the so-called no-energy-transfer regime known in classical nonlinear optics. By applying method of classical trajectories, we demonstrate that the analytical predictions of the Fano factors are in good agreement with the quantum results. On comparing second and higher harmonic generations in the no-energy-transfer regime, we show that the highest noise reduction is achieved in third-harmonic generation with the Fano-factor of the ...
Quantum oscillations in superconductors in magnetic field
Gvozdikov, Vladimir M.; Gvozdikova, Mariya V.
2000-07-01
The Aharonov-Bohm oscillations (ABO) of the free energy, the critical temperature, and the magnetic susceptibility in a stack of hollow mesoscopic cylinders are calculated. It is shown that sinusoidal (in flux) ABO crosses over to the parabolic Little-Parks oscillations (LPO) when the diameter of cylinders exceeds the coherence length. The exponential temperature behaviour of the magnetic susceptibility is like that found in Ag cylinders with thin Nb coating [Czech. J. Physics 46 (1996) 2317]. The formal analogy between oscillations of the free energy in the Aharonov-Bohm system in question and the de Haas-van Alphen oscillations (dHvAO) in layered superconductors is discussed.
Institute of Scientific and Technical Information of China (English)
WEI Gao-Feng; LONG Chao-Yun; LONG Zheng-Wen; QIN Shui-Jie
2008-01-01
In this paper,the isotropic charged harmonic oscillator in uniform magnetic field is researched in the non-commutative phase space;the corresponding exact energy is obtained,and the analytic eigenfunction is presented in terms of the confluent hypergeometric function.It is shown that in the non-commutative space,the isotropic charged harmonic oscillator in uniform magnetic field has the similar behaviors to the Landau problem.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
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.......1±2.6 and an encouragingly high QE of (48±14)% for the SCQDs....
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...
The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
Quintela, T. S.; Fabris, J. C.; Nogueira, J. A.
2016-09-01
In this work, we explicitly solve the problem of the harmonic oscillator in the classical limit of a minimal-length scenario. We show that (i) the motion equation of the oscillator is not linear anymore because the presence of a minimal length introduces an anarmonic term and (ii) its motion is described by a Jacobi sine elliptic function. Therefore, the motion is periodic with the same amplitude and with the new period depending on the minimal length. This result (the change in the period of oscillation) is very important since it enables us to find in a quite simple way the most relevant effect of the presence of a minimal length and consequently traces of the Planck-scale physics. We show applications of our results in spectroscopy and gravity.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities.
Effect of the shape of quantum dots on the third-harmonic generations
Li, Keyin; Guo, Kangxian; Liang, Litao
2017-02-01
The effect of the shape of quantum dots on the third-harmonic generations is theoretically investigated. Using the effective-mass approximation, calculations are performed employing methods of both the compact-density-matrix and the matrix diagonalization. We discuss the properties of the third-harmonic generations (THG) coefficients as a function of the incident photon frequency in elliptic and triangular shaped quantum dots. The results reveal that the shape of quantum dots has a great influence on the third-harmonic generations.
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 a min......) 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.......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...
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.
Waves and Oscillations A Prelude to Quantum Mechanics
Smith, Walter Fox
2010-01-01
Waves and oscillations permeate virtually every field of current physics research, are central to chemistry, and are essential to much of engineering. Furthermore, the concepts and mathematical techniques used for serious study of waves and oscillations form the foundation for quantum mechanics. Once they have mastered these ideas in a classical context, students will be ready to focus on the challenging concepts of quantum mechanics when they encounter them, rather than struggling with techniques. This lively textbook gives a thorough grounding in complex exponentials and the key aspects of d
Pulsed quantum interaction between two distant mechanical oscillators
Vostrosablin, Nikita; Rakhubovsky, Andrey A.; Filip, Radim
2016-12-01
Feasible setup for pulsed quantum nondemolition interaction between two distant mechanical oscillators through an optical or microwave mediator is proposed. The proposal uses homodyne measurement of the mediator and feedforward control of the mechanical oscillators to reach the interaction. To verify the quantum nature of the interaction, we investigate the Gaussian entanglement generated in the mechanical modes. We evaluate it under influence of mechanical bath and propagation loss for the mediator and propose ways to optimize the interaction. Finally, both currently available optomechanical and electromechanical platforms are numerically analyzed. The analysis shows that implementation is already feasible with current technology.
Generation of entanglement in quantum parametric oscillators using phase control.
Gonzalez-Henao, J C; Pugliese, E; Euzzor, S; Abdalah, S F; Meucci, R; Roversi, J A
2015-08-19
The control of quantum entanglement in systems in contact with environment plays an important role in information processing, cryptography and quantum computing. However, interactions with the environment, even when very weak, entail decoherence in the system with consequent loss of entanglement. Here we consider a system of two coupled oscillators in contact with a common heat bath and with a time dependent oscillation frequency. The possibility to control the entanglement of the oscillators by means of an external sinusoidal perturbation applied to the oscillation frequency has been theoretically explored. We demonstrate that the oscillators become entangled exactly in the region where the classical counterpart is unstable, otherwise when the classical system is stable, entanglement is not possible. Therefore, we can control the entanglement swapping from stable to unstable regions by adjusting amplitude and phase of our external controller. We also show that the entanglement rate is approximately proportional to the real part of the Floquet coefficient of the classical counterpart of the oscillators. Our results have the intriguing peculiarity of manipulating quantum information operating on a classical system.
Observation of quantum interference between separated mechanical oscillator wavepackets
Kienzler, D; Negnevitsky, V; Lo, H -Y; Marinelli, M; Nadlinger, D; Home, J P
2015-01-01
The ability of matter to be superposed at two different locations while being intrinsically connected by a quantum phase is among the most counterintuitive predictions of quantum physics. While such superpositions have been created for a variety of systems, the in-situ observation of the phase coherence has remained out of reach. Using a heralding measurement on a spin-oscillator entangled state, we project a mechanical trapped-ion oscillator into a superposition of two spatially separated states, a situation analogous to Schr\\"odinger's cat. Quantum interference is clearly observed by extracting the occupations of the energy levels. For larger states, we encounter problems in measuring the energy distribution, which we overcome by performing the analogous measurement in a squeezed Fock basis with each basis element stretched along the separation axis. Using 8 dB of squeezing we observe quantum interference for cat states with phase space separations of $\\Delta \\alpha = 15.6$, corresponding to wavepackets wit...
Use of videos for students to see the effect of changing gravity on harmonic oscillators
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
Verreault, René
2017-08-01
In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.
Quantum Dynamics of Mesoscopic Driven Duffing Oscillators in Rotating Frame
Guo, Lingzhen; Li, Xin-Qi
2010-01-01
We investigate the nonlinear dynamics of a mesoscopic driven Duffing oscillator in a quantum regime. We construct a bifurcation equation applicable in quantum regime. The predictions of our bifurcation equation agree with numerical results perfectly. In terms ofWigner function, we identify the nature of state near the bifurcation point, and extract the transition rate, which displays perfect scaling behavior with the driving distance to the bifurcation point.
Quantum coherent oscillations between two coupled bose-einstein condensates
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The theoretical investigation of quantum coherent atomic oscillations between two coupled Bose-Einstein condensates(BECs) is studied. We apply the inseparable wave function of time-space to describe two trapped BECs in a double-well magnetic trap. According to Thomas-Fermi approximation, dynamical equations of the interwell phase difference and population imbalance are obtained. Using numerical method, coherent atomic tunneling and macroscopic quantum self-trapping(MQST) effect are investigated.
Entanglement in systems of oscillators and quantum computations
Ozhigov, Yuri I.
2012-01-01
It is shown that quantum devices based only on oscillators cannot serve as the universal quantum computer, despite of entanglement in such devices, which we roughly estimate for the ideal case and for the harmful entanglement with photonic modes. We show that quasi-particles are the native shell for the entanglement already for ground state, in contast to the free electromagnetic field where vacuum state does not produce entanglement at all.
Deformed oscillator algebras for two dimensional quantum superintegrable systems
Bonatsos, Dennis; Kokkotas, K D; Bonatsos, Dennis
1994-01-01
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.
A new method based on the harmonic balance method for nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Chen, Y.M. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China); Liu, J.K. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China)], E-mail: jikeliu@hotmail.com
2007-08-27
The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.
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.
Relativistic quantum theories and neutrino oscillations
Energy Technology Data Exchange (ETDEWEB)
Keister, B D [Physics Division, 1015N, National Science Foundation, 4201 Wilson Blvd., Arlington, VA 22230 (United States); Polyzou, W N, E-mail: polyzou@uiowa.ed [Department of Physics and Astronomy, The University of Iowa, Iowa City, IA 52242 (United States)
2010-05-01
Neutrino oscillations are examined under the broad requirements of Poincare-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The aim of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable and how many factors that are important in principle end up being negligible in practice.
Dependence of s-waves on continuous dimension: The quantum oscillator and free systems
Energy Technology Data Exchange (ETDEWEB)
Wolf, K.B. [Centro de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Apartado Postal 48-3, Cuernavaca, Morelos 62251 (Mexico); Aceves-de-la-Cruz, F. [Departamento de Fisica, CUCEI, Universidad de Guadalajara, Av. Revolucion 1500, Guadalajara, Jalisco 44430 (Mexico)
2006-12-15
Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s-waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schroedinger equations with a fictitious centrifugal (for integer D{>=}4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0
Resonant behavior of a harmonic oscillator with fluctuating mass driven by a Mittag-Leffler noise
Zhong, Suchuan; Yang, Jianqiang; Zhang, Lu; Ma, Hong; Luo, Maokang
2017-02-01
The resonant behavior of a generalized Langevin equation (GLE) in the presence of a Mittag-Leffler noise is studied analytically in this paper. Considering that a GLE with a Mittag-Leffler friction kernel is very useful for modeling anomalous diffusion processes with long-memory and long-range dependence, and the surrounding molecules do not only collide with the Brownian particle but also adhere to the Brownian particle for random time. Thus, we consider the Brownian particle with fluctuating mass, and the fluctuations of the mass are modelled as a dichotomous noise. Applying the stochastic averaging method, we obtain the exact expression of the output amplitude gain of the system. By studying the impact of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude gain. The results indicate that the bona fide SR, the wide sense SR and the conventional SR phenomena occur in the proposed harmonic oscillator with fluctuating mass driven by Mittag-Leffler noise. It is found that when we consider the output amplitude gain versus the driving frequency, the phenomena of stochastic multi-resonance (SMR) with two, three and four peaks are observed, and the quadruple-peaks SR phenomenon had never been observed in previous literature. Besides, when we investigate the dependence of output amplitude gain on the memory exponent, the inverse stochastic resonance (ISR) phenomenon takes place, in contrast to the well-known phenomenon of stochastic resonance. Furthermore, we compare the corresponding ordinary harmonic oscillator without memory to our generalized model, and found that the properties of long-memory and long-range dependence endows our generalized model with more abundant dynamic behaviors than the ordinary harmonic oscillator without memory.
Beyond the quantum formalism: consequences of a neural-oscillator model to quantum cognition
de Barros, J Acacio
2013-01-01
In this paper we present a neural oscillator model of stimulus response theory that exhibits quantum-like behavior. We then show that without adding any additional assumptions, a quantum model constructed to fit observable pairwise correlations has no predictive power over the unknown triple moment, obtainable through the activation of multiple oscillators. We compare this with the results obtained in de Barros (2013), where a criteria of rationality gives optimal ranges for the triple moment.
Pupasov-Maksimov, Andrey M.
2015-12-01
It is shown that fundamental solutions Kσ(x , y ; t) = of the non-stationary Schrödinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator Hσ =Hosc + ΔVσ are expressed in terms of elementary functions only. An algorithm to calculate explicitly Kσ for an arbitrary increasing sequence of positive integers σ is given, and compact expressions for K { 1 , 2 } and K { 2 , 3 } are presented. A generalization of Mehler's formula to the case of exceptional Hermite polynomials is given.
Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device
Picone, Rico A. R.; Davis, Solomon; Devine, Cameron; Garbini, Joseph L.; Sidles, John A.
2017-04-01
We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
A least squares finite element scheme for transonic flow around harmonically oscillating airfoils
Cox, C. L.; Fix, G. J.; Gunzburger, M. D.
1983-01-01
The present investigation shows that a finite element scheme with a weighted least squares variational principle is applicable to the problem of transonic flow around a harmonically oscillating airfoil. For the flat plate case, numerical results compare favorably with the exact solution. The obtained numerical results for the transonic problem, for which an exact solution is not known, have the characteristics of known experimental results. It is demonstrated that the performance of the employed numerical method is independent of equation type (elliptic or hyperbolic) and frequency. The weighted least squares principle allows the appropriate modeling of singularities, which such a modeling of singularities is not possible with normal least squares.
Kurt, Arzu; Eryigit, Resul
2015-12-01
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one.
Guo, Feng; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Li, Heng
2016-10-01
Stochastic resonance in a fractional harmonic oscillator with random mass and signal-modulated noise is investigated. Applying linear system theory and the characteristics of the noises, the analysis expression of the mean output-amplitude-gain (OAG) is obtained. It is shown that the OAG varies non-monotonically with the increase of the intensity of the multiplicative dichotomous noise, with the increase of the frequency of the driving force, as well as with the increase of the system frequency. In addition, the OAG is a non-monotonic function of the system friction coefficient, as a function of the viscous damping coefficient, as a function of the fractional exponent.
Surface second harmonic generation of chiral molecules using three-coupled-oscillator model
Institute of Scientific and Technical Information of China (English)
Wang Xiao-Ou; Li Chun-Fei; Li Jun-Qing
2006-01-01
Based on the three-coupled-oscillator molecular model we proposed, the relation between the second-order susceptibilities of a chiral film and the molecular hyperpolarizabilities is given. The effect of microscopic parameters on the second-order susceptibilities is simulated numerically and the difference between the efficiencies of s-polarized second-harmonic fields induced by the left- and the right-handed circularly-polarized fundamental beams is discussed. The theoretical basis for studying second-order nonlinear optical properties of the chiral molecular media with a tripod-like structure is provided in this paper.
Classical and quantum interference in multiband optical Bloch oscillations
Longhi, S
2010-01-01
Classical and quantum interference of light propagating in arrays of coupled waveguides and undergoing multiband optical Bloch oscillations (BOs) with negligible Zener tunneling is theoretically investigated. In particular, it is shown that Mach-Zehnder-like interference effects spontaneously arise in multiband BOs owing to beam splitting and subsequent beam recombination occurring in one BO cycle. As a noteworthy example of quantum interference, we discuss the doubling of interference fringes in photon counting rates for a correlated photon pair undergoing two-band BOs, a phenomenon analogous to the manifestation of the de Broglie wavelength of an entangled biphoton state observed in quantum Mach-Zehnder interferometry.
Pseudoharmonic oscillator in quantum mechanics with a generalized uncertainty principle
Boukhellout, Abdelmalek
2013-01-01
The pseudoharmonic oscillator potential is studied in quantum mechanics with a generalized uncertainty relation characterized by the existence of a minimal length. By using the perturbative approach of Brau, we compute the correction to the energy spectrum in the first order of the minimal length parameter {\\beta}. The effect of the minimal length on the vibration-rotation of diatomic molecules is discussed.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015)] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
Directory of Open Access Journals (Sweden)
A.F. EL-Bassiouny
2006-01-01
Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.
Energy Technology Data Exchange (ETDEWEB)
Kurt, Arzu; Eryigit, Resul, E-mail: resul@ibu.edu.tr
2015-12-18
The master equation for a charged harmonic oscillator coupled to an electromagnetic reservoir is investigated up to fourth order in the interaction strength by using Krylov averaging method. The interaction is in the velocity-coupling form and includes a diamagnetic term. Exact analytical expressions for the second-, the third-, and the fourth-order contributions to mass renormalization, decay constant, normal and anomalous diffusion coefficients are obtained for the blackbody type environment. It is found that, generally, the third- and the fourth-order contributions have opposite signs when their magnitudes are comparable to that of the second-order one. - Highlights: • Exact analytical expressions for up to the fourth-order master equation are obtained. • High and low temperature limits of anomalous diffusion coefficients are elucidated. • Convergence range of the oscillator and the bath parameters discussed.
Pyragas, Viktoras; Pyragas, Kestutis
2015-08-01
In a recent paper [Phys. Rev. E 91, 012920 (2015), 10.1103/PhysRevE.91.012920] Olyaei and Wu have proposed a new chaos control method in which a target periodic orbit is approximated by a system of harmonic oscillators. We consider an application of such a controller to single-input single-output systems in the limit of an infinite number of oscillators. By evaluating the transfer function in this limit, we show that this controller transforms into the known extended time-delayed feedback controller. This finding gives rise to an approximate finite-dimensional theory of the extended time-delayed feedback control algorithm, which provides a simple method for estimating the leading Floquet exponents of controlled orbits. Numerical demonstrations are presented for the chaotic Rössler, Duffing, and Lorenz systems as well as the normal form of the Hopf bifurcation.
A quantum information theoretic analysis of three flavor neutrino oscillations
Banerjee, Subhashish; Srikanth, R; Hiesmayr, Beatrix C
2015-01-01
Correlations exhibited by neutrino oscillations are studied via quantum information theoretic quantities. We show that the strongest type of entanglement, genuine multipartite entanglement, is persistent in the flavour changing states. We prove the existence of Bell-type nonlocal features, in both its absolute and genuine avatars. Finally, we show that a measure of nonclassicality, dissension, which is a generalization of quantum discord to the tripartite case, is nonzero for almost the entire range of time in the evolution of an initial electron-neutrino. Via these quantum information theoretic quantities capturing different aspects of quantum correlations, we elucidate the differences between the flavour types, shedding light on the quantum-information theoretic aspects of the weak force.
Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks.
Ramasesh, V V; Flurin, E; Rudner, M; Siddiqi, I; Yao, N Y
2017-03-31
The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase, we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.
Harmonic bath averaged Hamiltonian: an efficient tool to capture quantum effects of large systems.
Yang, Yonggang; Liu, Xiaomeng; Meuwly, Markus; Xiao, Liantuan; Jia, Suotang
2012-11-26
Starting from a reaction path Hamiltonian, a suitably reduced harmonic bath averaged Hamiltonian is derived by averaging over all the normal mode coordinates. Generalization of the harmonic bath averaged Hamiltonian to any dimensions are performed and the feasibility to use a linear reaction path/surface are investigated and discussed. By use of a harmonic bath averaged Hamiltonian, the tunneling splitting and proton transfer dynamics of malonaldehyde is briefly discussed and shows that the harmonic bath averaged Hamiltonian is an efficient tool to capture quantum effects in larger systems.
Harmonic versus subharmonic patterns in a spatially forced oscillating chemical reaction.
Hammele, Martin; Zimmermann, Walter
2006-06-01
The effects of a spatially periodic forcing on an oscillating chemical reaction as described by the Lengyel-Epstein model are investigated. We find a surprising competition between two oscillating patterns, where one is harmonic and the other subharmonic with respect to the spatially periodic forcing. The occurrence of a subharmonic pattern is remarkable as well as its preference up to rather large values of the modulation amplitude. For small modulation amplitudes we derive from the model system a generic equation for the envelope of the oscillating reaction that includes an additional forcing contribution, compared to the amplitude equations known from previous studies in other systems. The analysis of this amplitude equation allows the derivation of analytical expressions even for the forcing corrections to the threshold and to the oscillation frequency, which are in a wide range of parameters in good agreement with the numerical analysis of the complete reaction equations. In the nonlinear regime beyond threshold, the subharmonic solutions exist in a finite range of the control parameter that has been determined by solving the reaction equations numerically for various sets of parameters.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.
Goto, Hayato
2016-02-22
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network
Goto, Hayato
2016-02-01
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems
Moncrief, Vincent; Maitra, Rachel
2012-01-01
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, w...
Probing anharmonicity of a quantum oscillator in an optomechanical cavity
Latmiral, Ludovico; Armata, Federico; Genoni, Marco G.; Pikovski, Igor; Kim, M. S.
2016-05-01
We present a way of measuring with high precision the anharmonicity of a quantum oscillator coupled to an optical field via radiation pressure. Our protocol uses a sequence of pulsed interactions to perform a loop in the phase space of the mechanical oscillator, which is prepared in a thermal state. We show how the optical field acquires a phase depending on the anharmonicity. Remarkably, one only needs small initial cooling of the mechanical motion to probe even small anharmonicities. Finally, by applying tools from quantum estimation theory, we calculate the ultimate bound on the estimation precision posed by quantum mechanics and compare it with the precision obtainable with feasible measurements such as homodyne and heterodyne detection on the cavity field. In particular we demonstrate that homodyne detection is nearly optimal in the limit of a large number of photons of the field and we discuss the estimation precision of small anharmonicities in terms of its signal-to-noise ratio.
Quantum unharmonic symmetrical oscillators using elliptic functions
Energy Technology Data Exchange (ETDEWEB)
Sanchez, A.M.; Bejarano, J.d.
1986-04-21
The authors study in the JWKB approximation the energy levels of the symmetric anharmonic oscillators V(x) Ax/sup 2/ + Bx/sup 4/ for different signs and values of A and B. Comparisons are made with published results for specific cases and with numerical calculations. An additional example is given of exact value, to add to the very rare catalogue of known examples.
Chang, C H; Li Xue Qian; Liu, Y; Ma, F C; Tao, Z; CHANG, Chao-Hsi; DAI, Wu-Sheng; LI, Xue-Qian; LIU, Yong; MA, Feng-Cai; TAO, Zhi-jian
1999-01-01
In this work we tried extensively to apply the EHNS postulation about the quantum mechanics violation effects induced by the quantum gravity of black holes to neutrino oscillations. The possibilities for observing such effects in the neutrino experiments (in progress and/or accessible in the near future) were discussed. Of them, an interesting one was outlined specially.
Pseudo Magnetic Faraday and Quantum Hall Effect In Oscillating Graphene
Bhagat, Anita; Mullen, Kieran
When a graphene layer is stressed, the strain changes the phase between sites in a tight binding model of the system. This phase can be viewed as a pseudo-magnetic vector potential. The corresponding pseudo-magnetic field has been experimentally verified in static cases. We examine the case of oscillating graphene ribbons and explore two new effects. The first is to investigate an oscillating pseudo-magnetic field that produces a quantum Hall effect: we calculate the I-V characteristic of an oscillating graphene nanoribbon as a function of frequency, and amplitude in both the oscillations and the applied driving voltage. Second, the time dependent pseudo-magnetic field should produce a pseudo-Faraday effect driving electrons in different valleys in opposite directions. In both cases, we make explicit calculations for experiment. This project was supported in part by the US National Science Foundation under Grant DMR-1310407.
Derivation of exact master equation with stochastic description: Dissipative harmonic oscillator
Li, Haifeng; Wang, Shikuan
2011-01-01
A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled and the master equation naturally comes out. Such an equation possesses the Lindblad form in which time dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation...
On the local virial theorems for linear and isotropic harmonic oscillator potentials in d dimensions
Energy Technology Data Exchange (ETDEWEB)
Bencheikh, K [Departement de Physique, Laboratoire de physique quantique et systemes dynamiques, Universite de Setif, Setif 19000 (Algeria); Nieto, L M, E-mail: bencheikh.kml@gmail.co [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2010-09-17
For the system of noninteracting fermions in a one-body potential V(r-vector), the local virial theorems (LVT) are relations, at a given point r-vector in space, between this potential, kinetic energy and particle densities. It was recently shown (Brack et al 2010 J. Phys. A: Math. Theor. 43 255204) that for d-dimensional linear and also for isotropic harmonic oscillator potentials these LVTs are exactly satisfied. We present alternative and simple proofs of these theorems, by consideration of the canonical or Bloch density matrix and its relation to the kinetic energy density. The explicit analytical forms of the Bloch density matrix are used for the above-mentioned potentials to achieve the proofs. For the case of linear potential, we obtain a more general result for the so-called semilocal virial theorem, and for the harmonic oscillator potential case we derive a new relationship between the diagonal part of the canonical bloch density and the kinetic energy density.
Haxton, Wick
2007-01-01
Semi-leptonic electroweak interactions in nuclei - such as \\beta decay, \\mu capture, charged- and neutral-current neutrino reactions, and electron scattering - are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |\\vec{p}|/M, where \\vec{p} and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q^2, where q is the magnitude of the three-momentum transfer. While results for such matrix elements a...
Reduction of Sub-Harmonic Oscillations in Flyback Converter for High Power Factor
Directory of Open Access Journals (Sweden)
Mr.M.SubbaRao,
2011-03-01
Full Text Available For High power factor (HPFoperation of flyback converter in continuous conduction mode(CCM, a variety of current mode control techniques, such as peak current control, Average current control andcharge control techniques has been analyzed. But these are suffer from stability problem due to presence of sub-harmonic oscillations and noise immunity. This can be overcome by using slope compensationtechnique, but it increases complexity .So the proposed technique in this paper i.e., a Single-Reset Integrator based line current shaping controller is a simple and accurate line current shaping controllerwith reduced sub-harmonic oscillations. In this paper presents the comparison between charge control technique with proposed control i.e., A Single-Reset Integrator based line current shaping controller for a 200 W,140V A.C input and 48V D.C output single phase flyback converter for HPF.MATLAB/Simulink software is used for implementation and simulation results shows the performance of proposed controller.
Quantum Electrodynamics Basis of Classical-Field High-Harmonic Generation Theory
Institute of Scientific and Technical Information of China (English)
王兵兵; 高靓辉; 傅盘铭; 郭东升; R. R. Freeman
2001-01-01
From the nonperturbative quantum electrodynamics theory, we derive the Landau-Dykhne formula which represents the quantum-mechanical formulation of the three-step model. These studies provide a basis for the classical-field approaches to high-order harmonic generation and justify some assumptions used in classical-field modelling.
DEFF Research Database (Denmark)
Taherkhani, Masoomeh; Gregersen, Niels; Willatzen, Morten
2017-01-01
The exciton oscillator strength (OS) in type-II quantum dot (QD) nanowires is calculated by using a fast and efficient method. We propose a new structure in Double-Well QD (DWQD) nanowire that considerably increases OS of type-II QDs which is a key parameter in optical quantum gating...... in the stimulated Raman adiabatic passage (STIRAP) process [1] for implementing quantum gates....
Phase-dependent quantum interference between different pathways in bichromatic harmonic generation
Institute of Scientific and Technical Information of China (English)
Cai Jun; Wang Li-Ming; Qiao Hao-Xue
2009-01-01
This paper studies the harmonic generation of the hydrogen atom subjected to a collinear bichromatic laser field by numerically solving the time-dependent Schr(o)dinger equation using the split-operator pseudo-spectral method.By adding a frequency variation to the additional field,the contributions of different pathways to particular order harmonic generation can be isolated.The quantum interference pattern between harmonic pathways,which influences the harmonic intensity,is found to be either constructive or destructive with respect to different relative phase of the two field components.Detailed description of up to the 35th-order harmonics and the harmonic pathways for a wide range of field parameters is presented.
Gupta, Shamik; Bandyopadhyay, Malay
2011-10-01
We obtain the quantum Langevin equation (QLE) of a charged quantum particle moving in a harmonic potential in the presence of a uniform external magnetic field and linearly coupled to a quantum heat bath through momentum variables. The bath is modeled as a collection of independent quantum harmonic oscillators. The QLE involves a random force which does not depend on the magnetic field, and a quantum-generalized classical Lorentz force. These features are also present in the QLE for the case of particle-bath coupling through coordinate variables. However, significant differences are also observed. For example, the mean force in the QLE is characterized by a memory function that depends explicitly on the magnetic field. The random force has a modified form with correlation and commutator different from those in the case of coordinate-coordinate coupling. Moreover, the coupling constants, in addition to appearing in the random force and in the mean force, also renormalize the inertial term and the harmonic potential term in the QLE.
Norrelykke, Simon F
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) Effects of finite sampling-rate and -time, described exactly here, are similar for other stochastic dynamical systems-e.g. motile micro-organisms and their time-lapse recorded trajectories. (ii) The same statistics is satisfied by any experimental system to the extent it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes effects of finite sampling rate and sampling time for these models as well. Finally, we give a brief discussion of nondimensio...
The performance characteristics of an irreversible quantum Otto harmonic refrigeration cycle
Institute of Scientific and Technical Information of China (English)
HE JiZhou; HE Xian; TANG Wei
2009-01-01
In this paper,an irreversible quantum Otto refrigeration cycle working with harmonic systems is estab-lished.Base on Heisenberg quantum master equation,the equations of motion for the set of harmonic systems thermodynamic observables are derived.The simulated diagrams of the quantum Otto refrig-eration cycle are plotted.The relationship between average power of friction,cooling rate,power input,and the time of adiabatic process is analyzed by using numerical calculation.Moreover,the influence of the heat conductance and the time of iso-frequency process on the performance of the cycle is dis-cussed.
The performance characteristics of an irreversible quantum Otto harmonic refrigeration cycle
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, an irreversible quantum Otto refrigeration cycle working with harmonic systems is established. Base on Heisenberg quantum master equation, the equations of motion for the set of harmonic systems thermodynamic observables are derived. The simulated diagrams of the quantum Otto refrigeration cycle are plotted. The relationship between average power of friction, cooling rate, power input, and the time of adiabatic process is analyzed by using numerical calculation. Moreover, the influence of the heat conductance and the time of iso-frequency process on the performance of the cycle is discussed.
Energy Technology Data Exchange (ETDEWEB)
Santhanam, Thalanayar S [Department of Physics Saint Louis University, Missouri, MO 63103 (United States); Santhanam, Balu [Department of Electrical and Computer Engineering, MSC01 1100 1, University of New Mexico Albuquerque, NM 87131-0001 (United States)], E-mail: santhats@slu.edu, E-mail: bsanthan@ece.unm.edu
2009-05-22
Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.
Single-atom quantum control of macroscopic mechanical oscillators
Bariani, F.; Otterbach, J.; Tan, Huatang; Meystre, P.
2014-01-01
We investigate a hybrid electromechanical system consisting of a pair of charged macroscopic mechanical oscillators coupled to a small ensemble of Rydberg atoms. The resonant dipole-dipole coupling between an internal atomic Rydberg transition and the mechanics allows cooling to its motional ground state with a single atom despite the considerable mass imbalance between the two subsystems. We show that the rich electronic spectrum of Rydberg atoms, combined with their high degree of optical control, paves the way towards implementing various quantum-control protocols for the mechanical oscillators.
Schwinger's oscillator method, supersymmetric quantum mechanics and massless particles
Directory of Open Access Journals (Sweden)
Mejía F. M.
2002-01-01
Full Text Available We consider Schwinger's method of angular momentum addition using the SU(2 algebra with both a fermionic and a bosonic oscillator. We show that the total spin states obtained are: one boson singlet state and an arbitrary number of spin-1/2 states, the later ones are energy degenerate. It means that we have in this case supersymmetric quantum mechanics and also the addition of angular momentum for massless particles. We review too the cases of two bosonic and two fermionic oscillators.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Rodes, J.J. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fuentes, R.; Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-02-16
The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to an oscillating charge in the electric field of a ring. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes and excellent agreement of the approximate frequencies and periodic solutions with the exact ones are demonstrated and discussed.
Macroscopic quantum oscillator based on a flux qubit
Energy Technology Data Exchange (ETDEWEB)
Singh, Mandip, E-mail: mandip@iisermohali.ac.in
2015-09-25
In this paper a macroscopic quantum oscillator is proposed, which consists of a flux-qubit in the form of a cantilever. The net magnetic flux threading through the flux-qubit and the mechanical degrees of freedom of the cantilever are naturally coupled. The coupling between the cantilever and the magnetic flux is controlled through an external magnetic field. The ground state of the flux-qubit-cantilever turns out to be an entangled quantum state, where the cantilever deflection and the magnetic flux are the entangled degrees of freedom. A variant, which is a special case of the flux-qubit-cantilever without a Josephson junction, is also discussed. - Highlights: • In this paper a flux-qubit-cantilever is proposed. • Coupling can be varied by an external magnetic field. • Ground state is a macroscopic entangled quantum state. • Ground state of the superconducting-loop-oscillator is a macroscopic quantum superposition. • Proposed scheme is based on a generalized quantum approach.
Quantum Oscillation in Narrow-Gap Topological Insulators.
Zhang, Long; Song, Xue-Yang; Wang, Fa
2016-01-29
The canonical understanding of quantum oscillation in metals is challenged by the observation of the de Haas-van Alphen effect in an insulator, SmB_{6} [Tan et al, Science 349, 287 (2015)]. Based on a two-band model with inverted band structure, we show that the periodically narrowing hybridization gap in magnetic fields can induce the oscillation of low-energy density of states in the bulk, which is observable provided that the activation energy is small and comparable to the Landau level spacing. Its temperature dependence strongly deviates from the Lifshitz-Kosevich theory. The nontrivial band topology manifests itself as a nonzero Berry phase in the oscillation pattern, which crosses over to a trivial Berry phase by increasing the temperature or the magnetic field. Further predictions to experiments are also proposed.
Gaiko, Nick V.; van Horssen, Wim T.
2016-11-01
In this paper, the free transverse vibrations of a vertically moving string with a harmonically time-varying length are studied. The string length variations are assumed to be small. By using the multiple-timescales perturbation method in conjunction with a Fourier series approach, we determine the resonance frequencies and derive the non-secularity conditions in the form of an infinite dimensional system of coupled ordinary differential equations. This system describes the long time behavior of the amplitudes of the oscillations. Then, the eigenvalues of the obtained system are studied by the Galerkin truncation method, and applicability of this method is discussed. Apart from this, the dynamic stability of the solution is investigated by an energy analysis. Additionally, resonance detuning is considered.
Directory of Open Access Journals (Sweden)
Rong Haiwu
2014-01-01
Full Text Available The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily.
Infrared and ultraviolet cutoffs in variational calculations with a harmonic oscillator basis
Coon, Sidney A
2013-01-01
I abstract from a recent publication [1] the motivations for, analysis in and conclusions of a study of the ultraviolet and infrared momentum regulators induced by the necessary truncation of the model spaces formed by a variational trial wave function. This trial function is built systematically from a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. Each model space is defined by a truncation of the expansion characterized by a counting number (N) and by the intrinsic scale ($\\hbar\\omega$) of the HO basis. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. In [1] we established practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces. Finally, I update this subject by mentioning recent work on our extrapolation prescriptions which have appeared since the submission of [1]. The numerical example chosen for this contribu...
Xiong, Huai; Kong, Xianren; Li, Haiqin; Yang, Zhenguo
2017-01-01
This paper considers dynamics of bilinear hysteretic systems, which are widely used for vibration control and vibration absorption such as magneto-rheological damper, metal-rubber. The method of incremental harmonic balance (IHB) technique that hysteresis is considered in the corrective term is improved in order to determine periodic solutions of bilinear hysteretic systems. The improved continuation method called two points tracing algorithm which is stable to the turning point makes the calculation more efficient for tracing amplitude-frequency response. Precise Hsu's method for analysing the stability of periodic solutions is introduced. The effects of different parameters of bilinear hysteretic oscillator on the response are discussed numerically. Some numerical simulations of considered bilinear hysteretic systems, including a single DOF and a 2DOF system, are effectively obtained by the modified IHB method and the results compare very well with the 4-oder Runge-Kutta method.
Fourth-order master equation for a charged harmonic oscillator coupled to an electromagnetic field
Kurt, Arzu; Eryigit, Resul
Using Krylov averaging method, we have derived a fourth-order master equation for a charged harmonic oscillator weakly coupled to an electromagnetic field. Interaction is assumed to be of velocity coupling type which also takes into account the diagmagnetic term. Exact analytical expressions have been obtained for the second, the third and the fourth-order corrections to the diffusion and the drift terms of the master equation. We examined the validity range of the second order master equation in terms of the coupling constant and the bath cutoff frequency and found that for the most values of those parameters, the contribution from the third and the fourth order terms have opposite signs and cancel each other. Inclusion of the third and the fourth-order terms is found to not change the structure of the master equation. Bolu, Turkey.
Deformed Relativistic Hartree Theory in Coordinate Space and in Harmonic Oscillator Basis
Institute of Scientific and Technical Information of China (English)
ZHOU Shan-Gui; MENG Jie; Shuhei YAMAJI; YANG Si-Chun
2000-01-01
The deformed relativistic Hartree theory (DRH) is solved both in coordinate space (DRH-c) and in harmonic oscillator basis (DRH-o). Results obtained from these two methods are compared in details. The DRH-c and DRH-o calculations give similar total binding energies, deformation, level structures and radii for nitrogen iso topes, while their descriptions on the density distributions for drip-line nuclei are very different. The large spatiai istributions of nucleon densities, which is crucial to understand a weakly bound system, can only be obtained by DRH-c calculations. This implies that the DRH theory should be solved in coordinate space in order to describe uclei close to the drip line.
Directory of Open Access Journals (Sweden)
V. Mohammadi
2015-01-01
Full Text Available We study the two-dimensional Klein-Gordon equation with spin symmetry in the presence of the superintegrable potentials. On Euclidean space, the SO(3 group generators of the Schrödinger-like equation with the Kepler-Coulomb potential are represented. In addition, by Levi-Civita transformation, the Schrödinger-like equation with harmonic oscillator which is dual to the Kepler-Coulomb potential and the SU(2 group generators of associated system are studied. Also, we construct the quadratic algebra of the hyperboloid superintegrable system. Then, we obtain the corresponding Casimir operators and the structure functions and the relativistic energy spectra of the corresponding quasi-Hamiltonians by using the quadratic algebra approach.
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
Bose-Einstein condensation in a two-component Bose gas with harmonic oscillator interaction
Abulseoud, A. A.; Abbas, A. H.; Galal, A. A.; El-Sherbini, Th M.
2016-07-01
In this article a system containing two species of identical bosons interacting via a harmonic oscillator potential is considered. It is assumed that the number of bosons of each species is the same and that bosons belonging to the same species repel each other while those belonging to different species attract. The Hamiltonian is diagonalized and the energy spectrum of the system is written down. The behaviour of the system in the thermodynamic limit is studied within the framework of the grand canonical ensemble, and thermodynamic parameters, such as the internal energy, entropy and specific heat capacity are calculated. It is shown that the system exhibits a single species Bose-Einstein condensation when the coupling strengths are equal and a dual species condensation when they are different.
Quantum-orbit analysis of high-order harmonic generation by resonant plasmon field enhancement
Shaaran, T; Lewenstein, M
2012-01-01
We perform a detailed analysis of high-order harmonic generation (HHG) in atoms within the strong field approximation (SFA) by considering spatially inhomogeneous monochromatic laser fields. We investigate how the individual pairs of quantum orbits contribute to the harmonic spectra. We show that in the case of inhomogeneous fields, the electron tunnels with two different canonical momenta. One of them leads to a higher cutoff and the other one develops a lower cutoff. Furthermore, we demonstrate that the quantum orbits have a very different behavior in comparison to the homogeneous field. We also conclude that in the case of the inhomogeneous fields, both odd and even harmonics are present in the HHG spectra. Within our model, we show that the HHG cutoff extends far beyond the semiclassical cutoff as a function of inhomogeneity strength. Our findings are in good agreement both with quantum mechanical and classical models.
Spatiotemporal separation of high harmonic radiation into two quantum path components
Energy Technology Data Exchange (ETDEWEB)
Gaarde, M. B.; Salin, F.; Constant, E.; Balcou, Ph.; Schafer, K. J.; Kulander, K. C.; L’Huillier, A.
1999-02-01
We present a spatio-temporal analysis of high harmonic generation, showing evidence for the presence of several quantum path contributions to the atomic dipole moment. We show that the harmonic radiation can largely be described as a sum of two fields having a phase proportional to the intensity of the generating field. We compare our results to recent experimental results demonstrating this separation. We show how the temporal and spatial coherence properties are influenced by this effect, and discuss how it could be used to obtain better control of the generated harmonic radiation.
Institute of Scientific and Technical Information of China (English)
侯邦品; 王顺金; 余万伦
2003-01-01
By using the algebraic structure in the operator dual space in the master equation for the driven dissipative harmonic oscillator, we have rewritten the master equation as a Schrodinger-like equation. Then we have used three gauge transformations and obtained an exact solution to the master equation in the particle number representation.
Ita, B. I.; Obong, H. P.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.
2014-11-01
The solutions of the Klein-Gordon equation with equal scalar and vector harmonic oscillator plus inverse quadratic potential for S-waves have been presented using the Nikiforov-Uvarov method. The bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms of the Laguerre polynomials.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...
Quantum inductance and high frequency oscillators in graphene nanoribbons.
Begliarbekov, Milan; Strauf, Stefan; Search, Christopher P
2011-04-22
Here we investigate high frequency AC transport through narrow graphene nanoribbons with top-gate potentials that form a localized quantum dot. We show that as a consequence of the finite dwell time of an electron inside the quantum dot (QD), the QD behaves like a classical inductor at sufficiently high frequencies ω ≥ GHz. When the geometric capacitance of the top-gate and the quantum capacitance of the nanoribbon are accounted for, the admittance of the device behaves like a classical serial RLC circuit with resonant frequencies ω ∼ 100-900 GHz and Q-factors greater than 10(6). These results indicate that graphene nanoribbons can serve as all-electronic ultra-high frequency oscillators and filters, thereby extending the reach of high frequency electronics into new domains.
A diffusion quantum Monte Carlo study of geometries and harmonic frequencies of molecules
Lu, Shih-I.
2004-01-01
This article describes an approach in determination of equilibrium geometries and harmonic frequencies of molecules by the Ornstein-Uhlenbeck diffusion quantum Monte Carlo method based on the floating spherical Gaussians. In conjunction with a projected and renormalized Hellmann-Feynman gradient and an electronic energy at variational Monte Carlo and diffusion quantum Monte Carlo, respectively, the quasi-Newton algorithm implemented with the Broyden-Fletcher-Goldfarb-Shanno updated Hessian was used to find the optimized molecular geometry. We applied this approach to N2 and H2O molecules. The geometry and harmonic frequencies calculated were consistent with some sophisticated ab initio calculated values within reasonable statistical uncertainty.
Haxton, Wick; Lunardini, Cecilia
2008-09-01
Semi-leptonic electroweak interactions in nuclei—such as β decay, μ capture, charged- and neutral-current neutrino reactions, and electron scattering—are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |p→|/M, where p→ and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in 12C. Program summaryProgram title: SevenOperators Catalogue identifier: AEAY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
Energy Technology Data Exchange (ETDEWEB)
Belendez, A., E-mail: a.belendez@ua.e [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Mendez, D.I. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Marini, S. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, I. [Departamento de Optica, Farmacologia y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2009-08-03
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
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......) samples with varying thickness of the capping layer. We determine radiative and nonradiative decay rates, from which we calculate an OS of 10.1+/-2.6 and an encouragingly high QE of (47+/-14)% for the SCQDs. The nonideal QE is attributed to nonradiative recombination at the etched nanohole interface...
Abdelmadjid Maireche
2015-01-01
The paper describes the deformed Hamiltonian for Schrödinger equation with mixed harmonic potential known by sextic potential and the corresponding spectrum of energies which depended with 3-new quantum numbers (j = l ± 1/2, l) and s = 1/2 in the non-commutativity infinitesimal parameter θ.
Directory of Open Access Journals (Sweden)
Yen-Yin Lin
2014-11-01
Full Text Available We report a multi-watt broadband continuous-wave multi-harmonic optical comb based on a frequency division-by-three singly-resonant optical parametric oscillator. This cw optical comb is frequency-stabilized with the help of a beat signal derived from the signal and frequency-doubled idler waves. The measured frequency fluctuation in one standard deviation is ~437 kHz. This is comparable to the linewidth of the pump laser which is a master-oscillator seeded Yb:doped fiber amplifier at ~1064 nm. The measured powers of the fundamental wave and the harmonic waves up to the 6th harmonic wave are 1.64 W, 0.77 W, 3.9 W, 0.78 W, 0.17 W, and 0.11 W, respectively. The total spectral width covered by this multi-harmonic comb is ~470 THz. When properly phased, this multi-harmonic optical comb can be expected to produce by Fourier synthesis a light source consisting of periodic optical field waveforms that have an envelope full-width at half-maximum of 1.59 fs in each period.
Particle quantum states with indefinite mass and neutrino oscillations
Lobanov, A E
2015-01-01
Spaces of particle states are constructed in such a way that charged leptons, neutrinos, as well as down- and up-type quarks are combined in multiplets with their components being considered as different quantum states of a single particle. In the theory based on the Lagrangian of fermion sector of the Standard Model modified with this approach the phenomenon of neutrino oscillations appears. By example of pion decay it is shown that the states of the neutrino, arising in the process of decay may be described by a superposition of states with identical momenta with very high accuracy.
Quantum and Classical Chirps in an Anharmonic Oscillator
Shalibo, Yoni; Barth, Ido; Friedland, Lazar; Bialczack, Radoslaw; Martinis, John M; Katz, Nadav
2011-01-01
We measure the state dynamics of a tunable anharmonic quantum system, the Josephson phase circuit, under the excitation of a frequency-chirped drive. At small anharmonicity, the state evolves like a wavepacket - a characteristic response in classical oscillators; in this regime we report exponentially enhanced lifetimes of highly excited states, held by the drive. At large anharmonicity, we observe sharp steps, corresponding to the excitation of discrete energy levels. The continuous transition between the two regimes is mapped by measuring the threshold of these two effects.
Vasil'ev, M. G.
2017-02-01
A technique for measuring the crystal cross-sectional area with a weight sensor based on the difference between its readings at the extreme rod positions in the stepwise and continuous modes of modulation of the pulling rate is proposed for the low-thermal gradient Czochralski method. A change in the crystallization rate at harmonic oscillations of the pulling rate is estimated with the aim of conserving the quality of the growing crystal for this measurement method.
Quantum phase transitions in the noncommutative Dirac Oscillator
Panella, O
2014-01-01
We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical value ($B_{\\text{cr}}$) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); $ii$) non-commutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\\text{cr}}^*$, where there is a second quantum phase transition (right-left), --this critical point disappears in the commutative limit--. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed.
A quantum mechanical model of "dark matter"
Belokurov, V V
2014-01-01
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
Germanas, D.; Stepšys, A.; Mickevičius, S.; Kalinauskas, R. K.
2017-06-01
This is a new version of the HOTB code designed to calculate three and four particle harmonic oscillator (HO) transformation brackets and their matrices. The new version uses the OpenMP parallel communication standard for calculations of harmonic oscillator transformation brackets. A package of Fortran code is presented. Calculation time of large matrices, orthogonality conditions and array of coefficients can be significantly reduced using effective parallel code. Other functionalities of the original code (for example calculation of single harmonic oscillator brackets) have not been modified.
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.
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Schröder, Markus; Schreiber, Michael; Kleinekathöfer, Ulrich
2007-03-21
Several techniques to solve a hierarchical set of equations of motion for propagating a reduced density matrix coupled to a thermal bath have been developed in recent years. This is either done using the path integral technique as in the original proposal by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1998)] or by the use of stochastic fields as done by Yan et al. [Chem. Phys. Lett. 395, 216 (2004)]. Based on the latter ansatz a compact derivation of the hierarchy using a decomposition of the spectral density function is given in the present contribution. The method is applied to calculate the time evolution of the reduced density matrix describing the motion in a harmonic, an anharmonic, and two coupled oscillators where each system is coupled to a thermal bath. Calculations to several orders in the system-bath coupling with two different truncations of the hierarchy are performed. The respective density matrices are used to calculate the time evolution of various system properties and the results are compared and discussed with a special focus on the convergence with respect to the truncation scheme applied.
Energy Technology Data Exchange (ETDEWEB)
Zhu Jiuyun (Department of Physics, Hunan Normal University, Hunan 410006 (China)); Kuang Leman (Theoretical Physics Division, Nankai Institute of Mathematics, Tianjin 300071 (China) Department of Physics and Institute of Physics, Hunan Normal University, Hunan 410081 (China))
1994-10-03
The even and odd coherent states (CSs) of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are constructed and some properties of these states are studied. Their quadrature squeezing and amplitude-squared squeezing are investigated in detail. It is shown that, while the squeezing behaviour of the even and odd CSs of the FDHSHO approaches that of the even and odd CSs of the usual harmonic oscillator as the dimension of the Hilbert space tends to infinity, this behaviour is nontrivally different if the dimension of the Hilbert space is finite. In the latter case, it is found that the even and odd CSs exhibit both amplitude-squared squeezing and quadrature squeezing. ((orig.))
Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators
Belenchia, Alessio; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2015-01-01
Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\\"odinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of opto-mechanical quantum oscillators is characterised 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 non-locality 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.
Le Yaouanc, A; Morénas, V; Oliver, L; Pène, O; Raynal, J C
2000-01-01
The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $\\delta m/m_b^2$.
Institute of Scientific and Technical Information of China (English)
WU Hao; FAN Hong-Yi
2008-01-01
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator (IEO) method to solving the energy spectrum of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1, X2]=[X2, X3]=[X3, X1]=iθ, and this method seems effective and concise.
Yuan, Jian-Hui; Chen, Ni; Mo, Hua; Zhang, Yan; Zhang, Zhi-Hai
2015-12-01
A detailed investigation of the second harmonic generation in symmetrical and asymmetrical Gaussian potential quantum wells under the influence of applied electric field by using the compact-density-matrix approach and the finite difference method. The results show that the second-harmonic generation susceptibility obtained in two cases can reach the magnitude of 10-4 m/V, which depend dramatically on the applied electric field and the structural parameters. Finally, the resonant peak and its corresponding to the resonant energy are also taken into account.
Van Diejen, J F
1997-01-01
Two families (type $A$ and type $B$) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type $A$) and the Laguerre polynomials (type $B$), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl.
Quantum properties of transverse pattern formation in second-harmonic generation
DEFF Research Database (Denmark)
Bache, Morten; Scotto, P.; Zambrini, R.;
2002-01-01
We investigate the spatial quantum noise properties of the one-dimensional transverse pattern formation instability in intracavity second-harmonic generation. The Q representation of a quasi-probability distribution is implemented in terms of nonlinear stochastic Langevin equations. We study...... these equations through extensive numerical simulations and analytically in the linearized limit. Our study, made below and above the threshold of pattern formation, is guided by a microscopic scheme of photon interaction underlying pattern formation in second-harmonic generation. Close to the threshold...
Energy Technology Data Exchange (ETDEWEB)
Cao Wei; Lu Peixiang; Lan Pengfei; Hong Weiyi; Wang Xinlin [Wuhan National Laboratory for Optoelectronics and School of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China)
2007-03-14
The time-frequency properties of high harmonic generation (HHG) driven by a bichromatic field consisting of a fundamental and a weak third harmonic field are investigated. The selection of an individual quantum path contributing to harmonic generation can be achieved by adjusting the relative phase between the two components of the driving field. The classical trajectory simulation of the strong-field electron dynamics is performed to analyse the physical process. Our calculations show that it is the control of the ionization step that leads to the quantum path selection. This quantum selection can be used to generate regular and strong attosecond pulses.
Can the oscillator strength of the quantum dot bandgap transition exceed unity?
Hens, Z.
2008-10-01
We discuss the apparent contradiction between the Thomas-Reiche-Kuhn sum rule for oscillator strengths and recent experimental data on the oscillator strength of the band gap transition of quantum dots. Starting from two simple single electron model systems, we show that the sum rule does not limit this oscillator strength to values below unity, or below the number of electrons in the highest occupied single electron state. The only upper limit the sum rule imposes on the oscillator strength of the quantum dot band gap transition is the total number of electrons in the quantum dot.
Green's Function for the Quartic Oscillator
Anderson, Robert L.
2016-01-01
In this paper, a quantum mechanical Green's function $G_{qo}(y_b,t_b;$ $y_a,t_a)$ for the quartic oscillator is presented. This result is built upon two previous papers: first [1], detailing the linearization of the quartic oscillator $(qo)$ to the harmonic oscillator $(ho)$, second [2], the integration of the classical action function for the quartic oscillator. Here an equivalent form for the quartic oscillator action function $S_{qo}(y_b,t_b;$ $y_a,t_a)$ in terms of harmonic oscillator var...
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.
The Harmonic Oscillator–A Simplified Approach
Directory of Open Access Journals (Sweden)
L. R. Ganesan
2008-01-01
Full Text Available Among the early problems in quantum chemistry, the one dimensional harmonic oscillator problem is an important one, providing a valuable exercise in the study of quantum mechanical methods. There are several approaches to this problem, the time honoured infinite series method, the ladder operator method etc. A method which is much shorter, mathematically simpler is presented here.
Zhai, Wangjian
2014-12-01
Electric-field-induced second-harmonic generation in asymmetrical Gaussian potential quantum wells is investigated using the effective mass approximation employing the compact density matrix method and the iterative approach. Our results show that the absolute value, the real part and the imaginary part of second-harmonic generation are greatly affected by the height of the Gaussian potential quantum wells, the range of the Gaussian confinement potential and the applied electric field. The relationship between the absolute value and the imaginary part of second-harmonic generation together with the relationship between the absolute value and the real part of second-harmonic generation is studied. It is found that no matter how the height of the Gaussian potential quantum wells, the range of the Gaussian confinement potential and the applied electric field vary, the resonant peaks of the absolute value of second-harmonic generation do not originate from the imaginary part but from the real part.
Muralidhar, K.
2014-03-01
Elementary particles are considered as local oscillators under the influence of zeropoint fields. Such oscillatory behavior of the particles leads to the deviations in their path of motion. The oscillations of the particle in general may be considered as complex rotations in complex vector space. The local particle harmonic oscillator is analyzed in the complex vector formalism considering the algebra of complex vectors. The particle spin is viewed as zeropoint angular momentum represented by a bivector. It has been shown that the particle spin plays an important role in the kinematical intrinsic or local motion of the particle. From the complex vector formalism of harmonic oscillator, for the first time, a relation between mass and bivector spin has been derived in the form . Where, is the angular velocity bivector of complex rotations, is the velocity of light. The unit vector acts as an operator on the idempotents and to give the eigen values The constant represents two fold nature of the equation corresponding to particle and antiparticle states. Further the above relation shows that the mass of the particle may be interpreted as a local spatial complex rotation in the rest frame. This gives an insight into the nature of fundamental particles. When a particle is observed from an arbitrary frame of reference, it has been shown that the spatial complex rotation dictates the relativistic particle motion. The mathematical structure of complex vectors in space and spacetime is developed.
CPT/Lorentz Invariance Violation and Quantum Field Theory
Arias, P; Gamboa-Rios, J; López-Sarrion, J; Méndez, F; Arias, Paola; Das, Ashok; Gamboa, Jorge; Lopez-Sarrion, Justo; Mendez, Fernando
2006-01-01
Analogies between the noncommutative harmonic oscillator and noncommutative fields are analyzed. Following this analogy we construct examples of quantum fields theories with explicit CPT and Lorentz symmetry breaking. Some applications to baryogenesis and neutrino oscillation are also discussed
Yuan, Jian-Hui; Zhang, Yan; Mo, Hua; Chen, Ni; Zhang, Zhihai
2015-12-01
The second-harmonic generation susceptibility in semiparabolic quantum wells with applied electric field is investigated theoretically. For the same topic studied by Zhang and Xie [Phys. Rev. B 68 (2003) 235315] [1], some new and reliable results are obtained by us. It is easily observed that the second harmonic generation susceptibility decreases and the blue shift of the resonance is induced with increasing of the frequencies of the confined potential. Moreover, a transition from a two-photon resonance to two single-photon resonances will appear adjusted by the frequencies of the confined potential. Similar results can also be obtained by controlling the applied electric field. Surprisingly, the second harmonic generation susceptibility is weakened in the presence of the electric field, which is in contrast to the conventional case. Finally, the resonant peak and its corresponding resonant energy are also taken into account.
DEFF Research Database (Denmark)
Han, Yong-Chang; Madsen, Lars Bojer
2010-01-01
We solve the time-dependent Schrödinger equation for atomic hydrogen in an intense field using spherical coordinates with a radial grid and a spherical harmonic basis for the angular part. We present the high-order harmonic spectra based on three different forms, the dipole, dipole velocity......, and acceleration forms, and two gauges, the length and velocity gauges. The relationships among the harmonic phases obtained from the Fourier transform of the three forms are discussed in detail. Although quantum mechanics is gauge invariant and the length and velocity gauges should give identical results, the two...... gauges present different computation efficiencies, which reflects the different behavior in terms of characteristics of the physical couplings acting in the two gauges. In order to obtain convergence, more angular momentum states are required in the length gauge, while more grid points are required...
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Energy Technology Data Exchange (ETDEWEB)
Campione, Salvatore, E-mail: sncampi@sandia.gov [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Center for Integrated Nanotechnologies (CINT), Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Department of Electrical Engineering and Computer Science, University of California Irvine, Irvine, California 92697 (United States); Benz, Alexander; Brener, Igal, E-mail: ibrener@sandia.gov [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Center for Integrated Nanotechnologies (CINT), Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Sinclair, Michael B. [Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States); Capolino, Filippo [Department of Electrical Engineering and Computer Science, University of California Irvine, Irvine, California 92697 (United States)
2014-03-31
We theoretically analyze the second harmonic generation capacity of two-dimensional periodic metamaterials comprising sub-wavelength resonators strongly coupled to intersubband transitions in quantum wells (QWs) at mid-infrared frequencies. The metamaterial is designed to support a fundamental resonance at ∼30 THz and an orthogonally polarized resonance at the second harmonic frequency (∼60 THz), while the asymmetric quantum well structure is designed to provide a large second order susceptibility. Upon continuous wave illumination at the fundamental frequency we observe second harmonic signals in both the forward and backward directions, with the forward efficiency being larger. We calculate the overall second harmonic conversion efficiency of the forward wave to be ∼1.3 × 10{sup −2} W/W{sup 2}—a remarkably large value, given the deep sub-wavelength dimensions of the QW structure (about 1/15th of the free space wavelength of 10 μm). The results shown in this Letter provide a strategy for designing easily fabricated sources across the entire infrared spectrum through proper choice of QW and resonator designs.
Camp, Seth; Gaarde, Mette B
2015-01-01
We present a theoretical study of the influence of resonant enhancement on quantum path dynamics in the generation of harmonics above and below the ionization threshold in helium. By varying the wavelength and intensity of the driving field from 425 nm to 500 nm and from 30 TW/cm${^2}$ to 140 TW/cm${^2}$, respectively, we identify enhancements of harmonics 7, 9, and 11 that correspond to multiphoton resonances between the ground state and the Stark shifted $1s2p$, $1s3p$, and $1s4p$ excited states. A time-frequency analysis of the emission shows that both the short and long quantum path contributions to the harmonic yield are enhanced through these bound state resonances. We analyze the sub-cycle time structure of the 9th harmonic yield in the vicinity of the resonances and find that on resonance the long trajectory contribution is phase shifted by approximately $\\pi/4$. Finally, we compare the single atom and the macroscopic response of a helium gas and find that while the sub-cycle time profiles are slightl...
Symmetry of bilinear master equations for a quantum oscillator
Tay, B. A.
2017-02-01
We study the most general continuous transformation on the generators of bilinear master equations of a quantum oscillator. We find that transformation operators that preserve the hermiticity of density operators and conserve the probability of reduced dynamics should be adjoint-symmetric, and they are not limited to the pure product of unitary operators in the bra and ket space but could be a mixture of them. We need to include the more general transformation operators to explore the full symmetry of generic reduced dynamics. We discuss how the operators are related to those considered in previous works, and illustrate how they leave the reduced dynamics form invariant, or map one into the other. The positive semidefinite requirement on the density operator can be imposed to give a valid range of transformation parameters.
Pauli-Heisenberg Oscillations in Electron Quantum Transport.
Thibault, Karl; Gabelli, Julien; Lupien, Christian; Reulet, Bertrand
2015-06-12
We measure the current fluctuations emitted by a normal-metal-insulator-normal-metal tunnel junction with a very wide bandwidth, from 0.3 to 13 GHz, down to very low temperature T=35 mK. This allows us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise (no dc bias, variable temperature) and shot noise (low temperature, variable dc voltage bias). Because of the very wide bandwidth of our measurement, we deduce the current-current correlator in the time domain. We observe the thermal decay of this correlator as well as its oscillations with a period h/eV, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.
Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode
Verhagen, E; Weis, S; Schliesser, A; Kippenberg, T J
2011-01-01
Quantum control of engineered mechanical oscillators can be achieved by coupling the oscillator to an auxiliary degree of freedom, provided that the coherent rate of energy exchange exceeds the decoherence rate of each of the two sub-systems. We achieve such quantum-coherent coupling between the mechanical and optical modes of a micro-optomechanical system. Simultaneously, the mechanical oscillator is cooled to an average occupancy of n = 1.7 \\pm 0.1 motional quanta. Pulsed optical excitation 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. These results provide a route towards the realization of efficient quantum interfaces between mechanical oscillators and optical fields.
On Noether's Theorem for the Invariant of the Time-Dependent Harmonic Oscillator
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru
2009-01-01
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
On Noether's theorem for the invariant of the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Abe, Sumiyoshi; Itto, Yuichi; Matsunaga, Mamoru [Department of Physical Engineering, Mie University, Mie 514-8507 (Japan)
2009-11-15
The time-dependent oscillator describing parametric oscillation, the concept of invariant and Noether's theorem are important issues in physics education. Here, it is shown how they can be interconnected in a simple and unified manner.
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu, E-mail: xbataxel@gmail.com [Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Wang, Jie, E-mail: wangjie@iun.edu [Department of Computer Information Systems, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2015-07-15
We obtain series solutions, the discrete spectrum, and supersymmetric partners for a quantum double-oscillator system. Its potential features a superposition of the one-parameter Mathews-Lakshmanan interaction and a one-parameter harmonic or inverse harmonic oscillator contribution. Furthermore, our results are transferred to a generalized Pöschl-Teller model that is isospectral to the double-oscillator system.
Molecular internal dynamics studied by quantum path interferences in high order harmonic generation
Energy Technology Data Exchange (ETDEWEB)
Zaïr, Amelle, E-mail: azair@imperial.ac.uk [Imperial College London, Department of Physics, Blackett Laboratory Laser Consortium, London SW7 2AZ (United Kingdom); Siegel, Thomas; Sukiasyan, Suren; Risoud, Francois; Brugnera, Leonardo; Hutchison, Christopher [Imperial College London, Department of Physics, Blackett Laboratory Laser Consortium, London SW7 2AZ (United Kingdom); Diveki, Zsolt; Auguste, Thierry [Service des Photons, Atomes et Molécules, CEA-Saclay, 91191 Gif-sur-Yvette (France); Tisch, John W.G. [Imperial College London, Department of Physics, Blackett Laboratory Laser Consortium, London SW7 2AZ (United Kingdom); Salières, Pascal [Service des Photons, Atomes et Molécules, CEA-Saclay, 91191 Gif-sur-Yvette (France); Ivanov, Misha Y.; Marangos, Jonathan P. [Imperial College London, Department of Physics, Blackett Laboratory Laser Consortium, London SW7 2AZ (United Kingdom)
2013-03-12
Highlights: ► Electronic trajectories in high order harmonic generation encodes attosecond and femtosecond molecular dynamical information. ► The observation of these quantum paths allows us to follow nuclear motion after ionization. ► Quantum paths interference encodes a signature of superposition of ionization channels. ► Quantum paths interference encodes a signature of transfer of population between channels due to laser coupling. ► Quantum paths interference is a promising technique to resolve ultra-fast dynamical processes after ionization. - Abstract: We investigate how short and long electron trajectory contributions to high harmonic emission and their interferences give access to information about intra-molecular dynamics. In the case of unaligned molecules, we show experimental evidence that the long trajectory contribution is more dependent upon the molecular species than the short one, providing a high sensitivity to cation nuclear dynamics from 100’s of as to a few fs after ionisation. Using theoretical approaches based on the strong field approximation and numerical integration of the time dependent Schrödinger equation, we examine how quantum path interferences encode electronic motion when the molecules are aligned. We show that the interferences are dependent upon which ionisation channels are involved and any superposition between them. In particular, quantum path interferences can encode signatures of electron dynamics if the laser field drives a coupling between the channels. Hence, molecular quantum path interferences are a promising method for attosecond spectroscopy, allowing the resolution of ultra-fast charge migration in molecules after ionisation in a self-referenced manner.
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 correlations of light due to a room temperature mechanical oscillator
Sudhir, Vivishek; Fedorov, Sergey A; Schuetz, Hendrik; Wilson, Dalziel J; Kippenberg, Tobias J
2016-01-01
The coupling of laser light to a mechanical oscillator via radiation pressure leads to the emergence of quantum mechanical correlations in the amplitude and phase quadrature of the laser beam. These correlations form a generic non-classical quantum resource which can be employed for quantum enhanced force metrology, and gives rise to ponderomotive squeezing in the limit of strong correlations. To date, this resource has only been observed in a handful of cryogenic cavity optomechanical experiments. Here, we demonstrate the ability to efficiently resolve optomechanical quantum correlations imprinted on an optical laser beam interacting with a room temperature nanomechanical oscillator. Direct measurement of the optical beam in a detuned homodyne detector ("variational readout") at frequencies far from the resonance frequency of the oscillator, reveal quantum correlations at a few percent level. We use these correlations to realize a $7\\%$ quantum-enhancement in thermal force estimation at room temperature. The...
Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems
Großardt, André; Ulbricht, Hendrik; Bassi, Angelo
2015-01-01
The Schr\\"odinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schr\\"odinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity, and can therefore be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schr\\"odinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.
Hamerly, Ryan; Jankowski, Marc; Fejer, Martin M; Yamamoto, Yoshihisa; Mabuchi, Hideo
2016-01-01
We develop reduced models that describe half-harmonic generation in a synchronously-pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simulton-like sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs. nondegenerate operation, and stability are derived and compared to numerical and experimental results.
Cosmology from quantum potential in a system of oscillating branes
Sepehri, Alireza
2016-11-01
Recently, some authors proposed a new mechanism which gets rid of the Big Bang singularity and shows that the age of the universe is infinite. In this paper, we will confirm their results and predict that the universe may expand and contract many N fundamental strings decay to N M0-anti-M0-branes. Then, M0-branes join each other and build a M8-anti-M8 system. This system is unstable, broken and two anti-M4-branes, a compactified M4-brane, a M3-brane in addition to one M0-brane are produced. The M3-brane wraps around the compactified M4-brane and both of them oscillate between two anti-M4-branes. Our universe is located on the M3-brane and interacts with other branes by exchanging the M0-brane and some scalars in transverse directions. By wrapping of M3-brane, the contraction epoch of universe starts and some higher order of derivatives of scalar fields in the relevant action of branes are produced which are responsible for generating the generalized uncertainty principle (GUP). By oscillating the compactified M4-M3-brane and approaching one of anti-M4-branes, one end of M3-brane glues to the anti-M4-brane and other end remains sticking and wrapping around M4-brane. Then, by getting away of the M4-M3 system, M4 rolls, wrapped M3 opens and expansion epoch of universe begins. By closing the M4 to anti-M4, the mass of some scalars become negative and they make a transition to tachyonic phase. To remove these states, M4 rebounds, rolls and M3 wraps around it again. At this stage, expansion branch ends and universe enters a contraction epoch again. This process is repeated many times and universe expands and contracts due to oscillation of branes. We obtain the scale factor of universe in this system and find that its values only at t →-∞ shrinks to zero. Thus, in our method, the Big Bang is replaced by the fundamental string and the age of universe is predicted to be infinite. Also, when tachyonic states disappear at the beginning of expansion branch, some extra
Ridolfo, A.; Stassi, R.; Di Stefano, O.
2017-06-01
We show that it is possible to realize quantum superpositions of switched-on and -off strong light-matter interaction in a single quantum dot- semiconductor microcavity system. Such superpositions enable the observation of counterintuitive quantum conditional dynamics effects. Situations are possible where cavity photons as well as the emitter luminescence display exponential decay but their joint detection probability exhibits vacuum Rabi oscillations. Remarkably, these quantum correlations are also present in the nonequilibrium steady state spectra of such coherently driven dissipative quantum systems.
Indian Academy of Sciences (India)
Y Ota; I Ohba
2002-08-01
The classical Dufﬁng oscillator is a dissipative chaotic system, and so there is not a deﬁnite Hamiltonian. We quantize the Dufﬁng oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can deﬁne a ‘Lyapunov exponent’, which corresponds to the classical one in the proper limit, and investigate the behavior of the system by varying the Planck constant effectively. We show that there exists a critical stage, where the behavior of the system crosses over from classical to quantum one.
The Quantum Mechanical Oscillator as a Possible Source of 1/f Fluctuations
Grueneis, Ferdinand
2012-01-01
We investigate consecutive absorption or emission of photons of the quantum mechanical harmonic oscillator as a possible source of 1/f fluctuations. Separating the absorption and emission process, we show that consecutively absorbed or emitted photons give rise to an intermittent stochastic process; thereby fluctuating clusters of photons are intermitted by distinct breaks. Let the number of photons in a cluster be m and the cluster size distribution be pm. We find that the intermittent process with a cluster size distribution pm proportional to m-2 generates a pure 1/f spectrum. We show that 1/f fluctuations are present in thermal equilibrium but average out to zero. As an example we investigate phonons as a possible origin of 1/f fluctuations in an extrinsic semiconductor. Acoustic phonons always produce a change in the volume; this affects the donor ionization energy modulating also the g-r process. We calculate the spectrum of such a modulated g-r process; thereby the intermittent character of phonon acti...
Energy Technology Data Exchange (ETDEWEB)
Belendez, A [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Pascual, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Neipp, C [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Belendez, T [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-02-15
A modified He's homotopy perturbation method is used to calculate higher-order analytical approximate solutions to the relativistic and Duffing-harmonic oscillators. The He's homotopy perturbation method is modified by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution in the second-order linear differential equation, and so on. We find this modified homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. The approximate formulae obtained show excellent agreement with the exact solutions, and are valid for small as well as large amplitudes of oscillation, including the limiting cases of amplitude approaching zero and infinity. For the relativistic oscillator, only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate frequency of less than 1.6% for small and large values of oscillation amplitude, while this relative error is 0.65% for two iterations with two harmonics and as low as 0.18% when three harmonics are considered in the second approximation. For the Duffing-harmonic oscillator the relative error is as low as 0.078% when the second approximation is considered. Comparison of the result obtained using this method with those obtained by the harmonic balance methods reveals that the former is very effective and convenient.
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Prospects of charged-oscillator quantum-state generation with Rydberg atoms
Stevenson, Robin; Minář, Jiří; Hofferberth, Sebastian; Lesanovsky, Igor
2016-10-01
We explore the possibility of engineering quantum states of a charged mechanical oscillator by coupling it to a stream of atoms in superpositions of high-lying Rydberg states. Our scheme relies on the driving of a two-phonon resonance within the oscillator by coupling it to an atomic two-photon transition. This approach effectuates a controllable open system dynamics on the oscillator that in principle permits versatile dissipative creation of squeezed and other nonclassical states which are central to sensing applications or for studies of fundamental questions concerning the boundary between classical and quantum-mechanical descriptions of macroscopic objects. We show that these features survive thermal coupling of the oscillator with the environment. We perform a detailed feasibility study finding that current state-of-the-art parameters result in atom-oscillator couplings which are too weak to efficiently implement the proposed oscillator state preparation protocol. Finally, we comment on ways to circumvent the present limitations.
Shevchenko, A B; Barabash, M Yu
2015-12-01
It is shown that at low temperatures, quantum oscillations of nanoscale structural inhomogeneities (the vertical Bloch line and the Bloch point) occur in the domain walls of cylindrical magnetic domains formed in a uniaxial magnetic film with strong magnetic anisotropy. The conditions for the excitation of these oscillations are determined.
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Bagchi, B. [Calcutta Univ. (India). Dept. of Applied Mathematics; Roy, P.K. [Department of Physics, Haldia Government College, Haldia 721 657, West Bengal (India)
1995-05-08
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.)).
Lu, Shih-I.
2004-06-01
Application of the Ornstein-Uhlenbeck diffusion quantum Monte Carlo method in combination with a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals to studies on the equilibrium structures and harmonic frequencies of ethane and ozone is presented. These Monte Carlo computed results are compared with those of experiments as well as the coupled cluster methods with the correlation consistent basis sets for the two molecules. For ozone, we also compare the Monte Carlo results with the results from multireference calculations.
Design of a second cyclotron harmonic gyrotron oscillator with photonic band-gap cavity
Energy Technology Data Exchange (ETDEWEB)
Liu Gaofeng; Chen Xiaoan; Tang Changjian, E-mail: angelchen765@163.com [College of Physical Science and Technology of Sichuan University, Chengdu 610065 (China)
2011-07-27
A photonic band-gap cavity (PBGC) gyrotron with a frequency of about 98 GHz is designed. Theoretical analyses and numerical calculations are made for the PBGC operating at fundamental and second cyclotron harmonic with a TE{sub 34} waveguide mode to demonstrate the beam-wave interaction. The results show that mode competition is successfully eliminated in the PBGC using mode selectivity and choosing the appropriate operating parameters. As a result, the second harmonic PBGC gyrotron operating at TE{sub 34} mode achieves a higher output efficiency than that of the fundamental. It is also demonstrated that, in the case of the chosen parameters for TE{sub 34} waveguide mode, the use of PBG structure in the second harmonic gyrotron brings about not only a lower operating B-field but also a weaker mode competition. The results show that the high-order electromagnetic mode can be developed to interact with the high cyclotron harmonic using the selectivity of the PBGC, which gives an encouraging outlook for the development of high-harmonic gyrotrons.
Difference oscillator in terms of the Meixner polynomials
Atakishiyev, Natig M.; Jafarov, Elchin I.; Nagiyev, Shakir M.; Wolf, Kurt B.
1998-07-01
We discuss a difference model of the linear harmonic oscillator based on the Meixner polynomials. As limit and special cases, it contains difference oscillator models in terms of the Kravchuk and Charlier polynomials, as well as the wavefunctions of the linear harmonic oscillator in quantum mechanics. We show that the dynamical group is SU(1,1) and construct explicitly the corresponding coherent state. The reproducing kernel for the wavefunctions of the Meixner model is also found.
Studies on the second-harmonic generations in cubical quantum dots with applied electric field
Energy Technology Data Exchange (ETDEWEB)
Shao Shuai [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Guo Kangxian, E-mail: axguo@sohu.co [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Zhang Zhihai; Li Ning; Peng Chao [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China)
2011-02-01
The second-harmonic generation (SHG) coefficient for cubical quantum dots (CQDs) with the applied electric field is theoretically investigated. Using the compact density-matrix approach and the iterative method, we get the analytical expression of the SHG coefficient. And the numerical calculations for the typical GaAs/AlAs CQDs are presented. The results show that the SHG coefficient can reach the magnitude of 10{sup -5} m/V, about two orders higher than that in spherical quantum dot system. More importantly, the SHG coefficient is not a monotonic function of the length L of CQDs as well as the applied field F. If we select suitable values of F and L, we will get a higher value of the SHG coefficient. In addition, the relaxation rate also affects the SHG coefficient obviously.
Cavity-mediated coupling of mechanical oscillators limited by quantum backaction
Spethmann, Nicolas; Schreppler, Sydney; Buchmann, Lukas; Stamper-Kurn, Dan M
2015-01-01
A complex quantum system can be constructed by coupling simple quantum elements to one another. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively quantum objects can be coupled by the exchange of real photons, particularly when driven within resonators that amplify interactions with a single electro-magnetic mode. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised. Here, we realize phase-coherent interactions between two spatially separated, near-ground-state mechanical oscillators within a driven optical cavity. We observe also the noise imparted by the optical coupling, which results in correlated mechanical fluctuations of the two oscillators. Achieving the quantum backaction dominated regime opens the door to numerous applications of cavity optomechanics with a complex mechanical system. Our results thereby illu...
Decoherence of a Quantum Nonlinear Oscillator Under a Non-zero Temperature Thermal Bath
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The characteristic time τD for decoherence process of a quantum nonlinear oscillator system under a nonzero temperature thermal bath is studied by expanding the linear entropy. By numerical analysis, it is shown that at a non-zero temperature, the quantum coherence decays much faster than at zero temperature. Moreover, the non-zero temperature thermal bath will bring a crucialsuppression to the quantum effects of the observables, which causes these quantum effects to become unable to persist up to the Ehrenfest time but is insufficient to destroy the quantum-classical transition.
Institute of Scientific and Technical Information of China (English)
ZHAI Zhi-Yuan; YANG Tao; PAN Xiao-Yin
2012-01-01
The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated. Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.%The propagator for an anisotropic two-dimension charged harmonic oscillator in the presence of a constant external magnetic field and a time-dependent electric field is exactly evaluated.Various special cases appearing in the literature can be obtained by properly setting the values of the parameters in our results.
Quantum noise of a Michelson-Sagnac interferometer with translucent mechanical oscillator
Yamamoto, Kazuhiro; Westphal, Tobias; Gossler, Stefan; Danzmann, Karsten; Schnabel, Roman; Somiya, Kentaro; Danilishin, Stefan L
2009-01-01
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 with high mechanical Q-values at room temperature have attracted attention as low thermal noise mechanical oscillators. However, the power reflectance of these membranes is much lower than unity 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 ...
Repelling, binding, and oscillating of two-particle discrete-time quantum walks
Wang, Qinghao; Li, Zhi-Jian
2016-10-01
In this paper, we investigate the effects of particle-particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle-particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.
Martinelli, M; Ducci, S; Gigan, S; Maitre, A; Fabre, C; Martinelli, Marcello; Treps, Nicolas; Ducci, Sara; Gigan, Sylvain; Maitre, Agnes; Fabre, Claude
2003-01-01
We study experimentally the spatial distribution of quantum noise in the twin beams produced by a type II Optical Parametric Oscillator operating in a confocal cavity above threshold. The measured intensity correlations are at the same time below the standard quantum limit and not uniformly distributed inside the beams. We show that this feature is an unambiguous evidence for the multimode and nonclassical character of the quantum state generated by the device.
Gajić, A.; Radovanović, J.; Milanović, V.; Indjin, D.; Ikonić, Z.
2014-02-01
A computational model for the optimization of the second order optical nonlinearities in GaInAs/AlInAs quantum cascade laser structures is presented. The set of structure parameters that lead to improved device performance was obtained through the implementation of the Genetic Algorithm. In the following step, the linear and second harmonic generation power were calculated by self-consistently solving the system of rate equations for carriers and photons. This rate equation system included both stimulated and simultaneous double photon absorption processes that occur between the levels relevant for second harmonic generation, and material-dependent effective mass, as well as band nonparabolicity, were taken into account. The developed method is general, in the sense that it can be applied to any higher order effect, which requires the photon density equation to be included. Specifically, we have addressed the optimization of the active region of a double quantum well In0.53Ga0.47As/Al0.48In0.52As structure and presented its output characteristics.
The time-dependent forced anisotropic oscillator in noncommutative phase space
Energy Technology Data Exchange (ETDEWEB)
Liang Mailin; Chen Qian, E-mail: mailinliang@yahoo.com.cn, E-mail: mailinliang@tju.edu.cn [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China)
2011-07-01
Wave functions of the time-dependent forced anisotropic harmonic oscillator in noncommutative phase space are derived using the linear transformation and unitary transformation methods. The energy spectrum is given for the stationary system. Further, quantum fluctuations and the squeezing effect are investigated. It is found that the anisotropic property of the harmonic oscillator in noncommutative space has the squeezing effect.
The dissipative quantum Duffing oscillator: A comparison of Floquet-based approaches
Energy Technology Data Exchange (ETDEWEB)
Vierheilig, Carmen, E-mail: Carmen.Vierheilig@physik.uni-regensburg.de [Institut fuer Theoretische Physik, Universitaet Regensburg, Universitaetsstrasse 31, 93040 Regensburg (Germany); Grifoni, Milena [Institut fuer Theoretische Physik, Universitaet Regensburg, Universitaetsstrasse 31, 93040 Regensburg (Germany)
2010-10-05
We study the dissipative quantum Duffing oscillator in the deep quantum regime with two different approaches: The first is based on the exact Floquet states of the linear oscillator and the nonlinearity is treated perturbatively. It well describes the nonlinear oscillator dynamics away from resonance. The second, in contrast, is applicable at and in the vicinity of an N-photon resonance and it exploits quasi-degenerate perturbation theory for the nonlinear oscillator in Floquet space. It is perturbative both in driving and nonlinearity. A combination of both approaches yields the possibility to cover a wide range of driving frequencies. As an example we discuss the dissipative dynamics of the Duffing oscillator near and at the one-photon resonance.
All-Optical Quantum Random Bit Generation from Intrinsically Binary Phase of Parametric Oscillators
Marandi, Alireza; Vodopyanov, Konstantin L; Byer, Robert L
2012-01-01
True random number generators (RNGs) are desirable for applications ranging from cryptogra- phy to computer simulations. Quantum phenomena prove to be attractive for physical RNGs due to their fundamental randomness and immunity to attack [1]- [5]. Optical parametric down conversion is an essential element in most quantum optical experiments including optical squeezing [9], and generation of entangled photons [10]. In an optical parametric oscillator (OPO), photons generated through spontaneous down conversion of the pump initiate the oscillation in the absence of other inputs [11, 12]. This quantum process is the dominant effect during the oscillation build-up, leading to selection of one of the two possible phase states above threshold in a degenerate OPO [13]. Building on this, we demonstrate a novel all-optical quantum RNG in which the photodetection is not a part of the random process, and no post processing is required for the generated bit sequence. We implement a synchronously pumped twin degenerate O...
Energy Technology Data Exchange (ETDEWEB)
Wang, Yang; Song, Hai-Ying; Liu, H.Y.; Liu, Shi-Bing, E-mail: sbliu@bjut.edu.cn
2017-07-12
Highlights: • Proposed a valid mechanism of high harmonic generation by laser grating target interaction: oscillation of equivalent electric dipole (OEED). • Found that there also exist harmonic emission at large emission angle but not just near-surface direction as the former researches had pointed out. • Show the process of the formation and motion of electron bunches at the grating-target surface irradiating with femtosecond laser pulse. - Abstract: We theoretically study high-order harmonic generation (HHG) from relativistically driven overdense plasma targets with rectangularly grating-structured surfaces by femtosecond laser pulses. Our particle-in-cell (PIC) simulations show that, under the conditions of low laser intensity and plasma density, the harmonics emit principally along small angles deviating from the target surface. Further investigation of the surface electron dynamics reveals that the electron bunches are formed by the interaction between the laser field and the target surface, giving rise to the oscillation of equivalent electric-dipole (OEED), which enhances specific harmonic orders. Our work helps understand the mechanism of harmonic emissions from grating targets and the distinction from the planar harmonic scheme.
Quantum mechanics using Fradkin's representation
Shajesh, K V; Milton, Kimball A.
2005-01-01
Fradkin's representation is a general method of attacking problems in quantum field theory, having as its basis the functional approach of Schwinger. As a pedagogical illustration of that method, we explicitly formulate it for quantum mechanics (field theory in one dimension) and apply it to the solution of Schrodinger's equation for the quantum harmonic oscillator.
Raghavan, S.; Smerzi, A.; Fantoni, S.; Shenoy, S. R.
1999-01-01
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 3He-B and the internal Josephson effect in 3He-A are also discussed.
Directory of Open Access Journals (Sweden)
Katarzyna Kolczyńska
2010-07-01
Full Text Available The HOMA (Harmonic Oscillator Model of Aromaticity index, reformulated in 1993, has been very often applied to describe π-electron delocalization for mono- and polycyclic π-electron systems. However, different measures of π-electron delocalization were employed for the CC, CX, and XY bonds, and this index seems to be inappropriate for compounds containing heteroatoms. In order to describe properly various resonance effects (σ-π hyperconjugation, n-π conjugation, π-π conjugation, and aromaticity possible for heteroatomic π-electron systems, some modifications, based on the original HOMA idea, were proposed and tested for simple DFT structures containing C, N, and O atoms. An abbreviation HOMED was used for the modified index.
Yu, Rong Mei; Zan, Li Rong; Jiao, Li Guang; Ho, Yew Kam
2017-09-01
Spatially confined atoms have been extensively investigated to model atomic systems in extreme pressures. For the simplest hydrogen-like atoms and isotropic harmonic oscillators, numerous physical quantities have been established with very high accuracy. However, the expectation value of employed the basis expansion method with cut-off Slater-type orbitals to investigate these two confined systems. Accurate values for several low-lying bound states were obtained by carefully examining the convergence with respect to the size of basis. A scaling law for < rn \\rangle was derived and it is used to verify the accuracy of numerical results. Comparison with other calculations show that the present results establish benchmark values for this quantity, which may be useful in future studies.
Li, Tongcang
2016-01-01
Schr\\"odinger's thought experiment to prepare a cat in a superposition of both alive and dead states reveals profound consequences of quantum mechanics and has attracted enormous interests. Here we propose a straightforward method to create quantum superposition states of a living microorganism by putting a small bacterium on top of an electromechanical oscillator. Our proposal is based on recent developments that the center-of-mass oscillation of a 15-$\\mu$m-diameter aluminium membrane has been cooled to its quantum ground state [Nature 475, 359 (2011)], and entangled with a microwave field [Science, 342, 710 (2013)]. A microorganism with a mass much smaller than the mass of the electromechanical membrane will not significantly affect the quality factor of the membrane and can be cooled to the quantum ground state together with the membrane. Quantum superposition and teleportation of its center-of-mass motion state can be realized with the help of superconducting microwave circuits. More importantly, the int...
Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals.
Zhang, Yi; Bulmash, Daniel; Hosur, Pavan; Potter, Andrew C; Vishwanath, Ashvin
2016-04-01
We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools--semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals--we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces. Based on these methods, we identify a 'magic' magnetic-field angle where quantum oscillations become independent of sample thickness, with striking experimental implications. We also analyze the stability of these quantum oscillations to disorder, and show that the high-field oscillations are expected to persist in samples whose thickness parametrically exceeds the quantum mean free path.
Knight, P L
1983-01-01
Concepts of Quantum Optics is a coherent and sequential coverage of some real insight into quantum physics. This book is divided into six chapters, and begins with an overview of the principles and concepts of radiation and quanta, with an emphasis on the significance of the Maxwell's electromagnetic theory of light. The next chapter describes first the properties of the radiation field in a bounded cavity, showing how each cavity field mode has the characteristics of a simple harmonic oscillator and how each can be quantized using known results for the quantum harmonic oscillator. This chapte
Robust identification of harmonic oscillator parameters using the adjoint Fokker-Planck equation
Boujo, E.; Noiray, N.
2017-04-01
We present a model-based output-only method for identifying from time series the parameters governing the dynamics of stochastically forced oscillators. In this context, suitable models of the oscillator's damping and stiffness properties are postulated, guided by physical understanding of the oscillatory phenomena. The temporal dynamics and the probability density function of the oscillation amplitude are described by a Langevin equation and its associated Fokker-Planck equation, respectively. One method consists in fitting the postulated analytical drift and diffusion coefficients with their estimated values, obtained from data processing by taking the short-time limit of the first two transition moments. However, this limit estimation loses robustness in some situations-for instance when the data are band-pass filtered to isolate the spectral contents of the oscillatory phenomena of interest. In this paper, we use a robust alternative where the adjoint Fokker-Planck equation is solved to compute Kramers-Moyal coefficients exactly, and an iterative optimization yields the parameters that best fit the observed statistics simultaneously in a wide range of amplitudes and time scales. The method is illustrated with a stochastic Van der Pol oscillator serving as a prototypical model of thermoacoustic instabilities in practical combustors, where system identification is highly relevant to control.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...
Castro-Palacio, Juan Carlos; Gimenez, Marcos H; Monsoriu, Juan A
2012-01-01
The mobile acceleration sensor has been used to in Physics experiments on free and damped oscillations. Results for the period, frequency, spring constant and damping constant match very well to measurements obtained by other methods. The Accelerometer Monitor application for Android has been used to get the outputs of the sensor. Perspectives for the Physics laboratory have also been discussed.
Directory of Open Access Journals (Sweden)
M. K. Bahar
2013-01-01
Full Text Available Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.
Quantum ion-acoustic oscillations in single-walled carbon nanotubes
Energy Technology Data Exchange (ETDEWEB)
Khan, S.A. [Kyoto Univ., Katsura (Japan). Graduate School of Engineering; Quaid-i-Azam Univ., Islamabad (Pakistan). National Centre for Physics; Iqbal, Z. [University of Management and Technology, Sialkot (Pakistan); Wazir, Z. [Riphah International Univ., Islamabad (Pakistan). Dept. of Basic Sciences; Rehman, Aman ur [Pakistan Institute of Engineering and Applied Sciences (PIEAS), Islamabad (Pakistan)
2016-08-01
Quantum ion-acoustic oscillations in single-walled carbon nanotubes are studied by employing a quantum hydrodynamics model. The dispersion equation is obtained by Fourier transformation, which exhibits the existence of quantum ion-acoustic wave affected by change of density balance due to presence of positive or negative heavy species as stationary ion clusters and wave potential at equilibrium. The numerical results are presented, and the role of quantum degeneracy, nanotube geometry, electron exchange-correlation effects, and concentration and polarity of heavy species on wave dispersion is pointed out for typical systems of interest.
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.
Kraft, Manuel; Hein, Sven M.; Lehnert, Judith; Schöll, Eckehard; Hughes, Stephen; Knorr, Andreas
2016-08-01
Quantum coherent feedback control is a measurement-free control method fully preserving quantum coherence. In this paper we show how time-delayed quantum coherent feedback can be used to control the degree of squeezing in the output field of a cavity containing a degenerate parametric oscillator. We focus on the specific situation of Pyragas-type feedback control where time-delayed signals are fed back directly into the quantum system. Our results show how time-delayed feedback can enhance or decrease the degree of squeezing as a function of time delay and feedback strength.
Bates, David Robert
1962-01-01
Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postula
Vierheilig, Carmen; Grifoni, Milena
2010-01-01
We consider a qubit coupled to a nonlinear quantum oscillator, the latter coupled to an Ohmic bath, and investigate the qubit dynamics. This composed system can be mapped onto that of a qubit coupled to an effective bath. An approximate mapping procedure to determine the spectral density of the effective bath is given. Specifically, within a linear response approximation the effective spectral density is given by the knowledge of the linear susceptibility of the nonlinear quantum oscillator. To determine the actual form of the susceptibility, we consider its periodically driven counterpart, the problem of the quantum Duffing oscillator within linear response theory in the driving amplitude. Knowing the effective spectral density, the qubit dynamics is investigated. In particular, an analytic formula for the qubit's population difference is derived. Within the regime of validity of our theory, a very good agreement is found with predictions obtained from a Bloch-Redfield master equation approach applied to the...
Observation of quantum oscillation of work function in ultrathin-metal/semiconductor junctions
Energy Technology Data Exchange (ETDEWEB)
Takhar, Kuldeep; Meer, Mudassar; Khachariya, Dolar; Ganguly, Swaroop; Saha, Dipankar, E-mail: dipankarsaha@iitb.ac.in [Applied Quantum Mechanics Laboratory, Centre of Excellence in Nanoelectronics, Department of Electrical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076 (India)
2015-09-15
Quantization in energy level due to confinement is generally observed for semiconductors. This property is used for various quantum devices, and it helps to improve the characteristics of conventional devices. Here, the authors have demonstrated the quantum size effects in ultrathin metal (Ni) layers sandwiched between two large band-gap materials. The metal work function is found to oscillate as a function of its thickness. The thermionic emission current bears the signature of the oscillating work function, which has a linear relationship with barrier heights. This methodology allows direct observation of quantum oscillations in metals at room temperature using a Schottky diode and electrical measurements using source-measure-units. The observed phenomena can provide additional mechanism to tune the barrier height of metal/semiconductor junctions, which are used for various electronic devices.
Floß, Johannes; Averbukh, Ilya Sh
2016-05-19
We describe a universal behavior of linear molecules excited by a periodic train of short laser pulses under conditions close to the quantum resonance. The quantum resonance effect causes an unlimited ballistic growth of the angular momentum. We show that a disturbance of the quantum resonance, either by the centrifugal distortion of the rotating molecules or a controlled detuning of the pulse train period from the so-called rotational revival time, eventually halts the growth by causing Anderson localization beyond a critical value of the angular momentum, the Anderson wall. Below the wall, the rotational excitation oscillates with the number of pulses due to a mechanism similar to Bloch oscillations in crystalline solids. We suggest optical experiments capable of observing the rotational Anderson wall and Bloch oscillations at near-ambient conditions with the help of existing laser technology.
Quantum Walks as simulators of neutrino oscillations in vacuum and matter
Di Molfetta, Giuseppe
2016-01-01
We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to explore these effects in extreme conditions, such as the solar interior or supernovae, in a complementary way to existing experiments.
Quantum walks as simulators of neutrino oscillations in a vacuum and matter
Di Molfetta, G.; Pérez, A.
2016-10-01
We analyze the simulation of Dirac neutrino oscillations using quantum walks, both in a vacuum and in matter. We show that this simulation, in the continuum limit, reproduces a set of coupled Dirac equations that describe neutrino flavor oscillations, and we make use of this to establish a connection with neutrino phenomenology, thus allowing one to fix the parameters of the simulation for a given neutrino experiment. We also analyze how matter effects for neutrino propagation can be simulated in the quantum walk. In this way, important features, such as the MSW effect, can be incorporated. Thus, the simulation of neutrino oscillations with the help of quantum walks might be useful to illustrate these effects in extreme conditions, such as the solar interior or supernovae.
Spin-flavor oscillations of Dirac neutrinos described by relativistic quantum mechanics
Dvornikov, Maxim
2010-01-01
We study spin-flavor oscillations of Dirac neutrinos in matter and magnetic field using the method of relativistic quantum mechanics. We start from the exact solution of the wave equation for a massive neutrino, taking into account external fields. Then we derive an effective Hamiltonian governing neutrino spin-flavor oscillations. We demonstrate the consistency of our approach with the commonly used quantum mechanical method. Our correction to the usual effective Hamiltonian results in the appearance of a new resonance in neutrino oscillations. We discuss applications to spin-flavor neutrino oscillations in the expanding envelope of a supernova. In particular, transitions between right-handed electron neutrinos and sterile neutrinos are studied for a realistic background matter and magnetic field distributions. We also analyze the influence of other factors such as a longitudinal magnetic field, matter polarization, and the non-standard contributions to the neutrino effective potential.
Liu, Li; Zhang, Liang-Ying; Cao, Li
2009-10-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Ornstein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3) Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
Institute of Scientific and Technical Information of China (English)
Liu Li; Zhang Liang-Ying; Cao Li
2009-01-01
The diffusion in a harmonic oscillator driven by coloured noises ζ(t) and η(t) with coloured cross-correlation in which one of the noises is modulated by a biased periodic signal is investigated. The exact expression of diffusion coefficient d as a function of noise parameter, signal parameter, and oscillator frequency is derived. The findings in this paper are as follows. 1) The curves of d versus noise intensity D and d versus noises cross-correlation time τ_3 exist as two different phases. The transition between the two phases arises from the change of the cross-correlation coefficient λ of the two Orustein-Uhlenbeck (O-U) noises. 2) Changing the value of τ3, the curves of d versus Q, the intensity of colored noise that is modulated by the signal, can transform from a phase having a minimum to a monotonic phase. 3)Changing the value of signal amplitude A, d versus Q curves can transform from a phase having a minimum to a monotonic phase. The above-mentioned results demonstrate that a like noise-induced transition appears in the model.
Bajer, Jirí; Miranowicz, Adam
2000-06-01
Second-harmonic generation in the no-energy-transfer regime can be a source of quasi-stationary sub-Poissonian light as was recently shown by Bajer et al (Bajer J, Haderka O and Perina J 1999 J. Opt. B: Quantum Semiclass. Opt. 1 529). We generalize their results for higher-harmonic generation by applying the numerical method of Hamiltonian diagonalization and the analytical semiclassical description of classical trajectories. The quasi-stationary behaviour of the sub-Poissonian photocount noise in the no-energy-transfer regime is explained. An approximate formula for the Fano factor is derived for arbitrary harmonics. It is predicted that the deepest quasi-stationary reduction of photocount noise in the no-energy-transfer regime is achieved in the third-harmonic generation.
Quantum information entropies of ultracold atomic gases in a harmonic trap
Indian Academy of Sciences (India)
Tutul Biswas; Tarun Kanti Ghosh
2011-10-01
The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We ﬁnd that sum of the position and momentum space information entropies of these quantum systems containing atoms conﬁned in a $D(≤ 3)$-dimensional harmonic trap has a universal form as $S^{(D)}_t = N(a D − b ln N)$, where ∼ 2.332 and = 2 for interacting bosonic systems and a ∼ 1.982 and = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.
Energy Technology Data Exchange (ETDEWEB)
Thantu, Napoleon; Schley, Robert Scott; B. L. Justus
2003-05-01
Two-photon excited emission centered at 379-426 nm in photodarkening borosilicate glass doped with CuCl nanocrystalline quantum dots at room temperature has been observed. The emission is detected in the direction of the fundamental near-infrared beam. Time- and frequency-resolved measurements at room temperature and 77 K indicate that the emission is largely coherent light characteristic of second harmonic generation (SHG). An average conversion efficiency of ~10-10 is obtained for a 2 mm thick sample. The observed SHG can originate in the individual noncentrosymmetric nanocrystals, leading to a bulk-like contribution, and at the nanocrystal-glass interface, leading to a surface contribution. The bulk-like conversion efficiency is estimated using previously reported values of coherence length (5m) and bulk nonlinear susceptibility. This bulk-like conversion efficiency estimate is found to be smaller than the measured value, suggesting a more prominent surface contribution.
Directory of Open Access Journals (Sweden)
Andrea V. Bragas
2011-03-01
Full Text Available We report the enhancement of the optical second harmonic signal in non-centrosymmetric semiconductor CdS quantum dots, when they are placed in close contact with isolated silver nanoparticles. The intensity enhancement is about 1000. We also show that the enhancement increases when the incoming laser frequency $omega$ is tuned toward the spectral position of the silver plasmon at $2omega$, proving that the silver nanoparticle modifies the nonlinear emission.Received: 8 March 2011, Accepted: 30 May 2011; Edited by: L. Viña; Reviewed by: R. Gordon, Department of Electrical and Computer Engineering, University of Victoria, British Columbia, Canada; DOI: 10.4279/PIP.030002Cite as: P. M. Jais, C. von Bilderling, A. V. Bragas, Papers in Physics 3, 030002 (2011
Second-harmonic generation in asymmetric quantum dots in the presence of a static magnetic field
Institute of Scientific and Technical Information of China (English)
Li Xue-Chao; Wang An-Min; Wang Zhao-Liang; Yang Yang
2012-01-01
The second-harmonic generation (SHG) coefficient in an asymmetric quantum dot (QD) with a static magnetic field is theoretically investigated.Within the framework of the effective-mass approximation,we obtain the confined wave functions and energies of electrons in the QD.We also obtain the SHG coefficient by the compact-density-matrix approach and the iterative method.The numerical results for the typical GaAs/AlGaAs QD show that the SHG coefficient depends strongly on the magnitude of magnetic field,parameters of the asymmetric potential and the radius of the QD.The resonant peak shifts with the magnetic field or the radius of the QD changing.
Correlation effects on the energy spectra of quantum dot electrons with harmonic model interactions
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The low-lying excitation energy spectra of two, three and five quantum dot electrons with harmonic model interactions in a large magnetic field are calculated by the Hartree-Fock(HF) methods. Correlation effects on the energy level structures are investigated by comparing the HF results with the exact ones. It is found that the pure collective excitations(center-of-mass mode quanta) existing in the exact energy spectra do not appear in the HF energy spectra. The degeneracies of energy levels are also related to the correlation interactions, especially in the energy spectrum of two electrons. In the cases of more than two electrons, as the electron-electron interaction strength is increased the HF energy levels exhibit more complex crossings than the exact ones.
Role of quantum trajectory in high-order harmonic generation in the Keldysh multiphoton regime.
Li, Peng-Cheng; Jiao, Yuan-Xiang; Zhou, Xiao-Xin; Chu, Shih-I
2016-06-27
We present a systematic study of spectral and temporal structure of high-order harmonic generation (HHG) by solving accurately the time-dependent Schrödinger equation for a hydrogen atom in the multiphoton regime where the Keldysh parameter is greater unity. Combining with a time-frequency transform and an extended semiclassical analysis, we explore the role of quantum trajectory in HHG. We find that the time-frequency spectra of the HHG plateau near cutoff exhibit a decrease in intensity associated with the short- and long-trajectories when the ionization process is pushed from the multiphoton regime into the tunneling regime. This implies that the harmonic emission spectra in the region of the HHG plateau near and before the cutoff are suppressed. To see the generality of this prediction, we also present a time-dependent density-functional theoretical study of the effect of correlated multi-electron responses on the spectral and temporal structure of the HHG plateau of the Ar atom.
Electric dipole moment oscillations in Aharonov-Bohm quantum rings
Alexeev, A. M.; Portnoi, M. E.
2012-01-01
Magneto-oscillations of the electric dipole moment are predicted and analyzed for a single-electron nanoscale ring pierced by a magnetic flux (an Aharonov-Bohm ring) and subjected to an electric field in the ring's plane. These oscillations are accompanied by periodic changes in the selection rules for inter-level optical transitions in the ring allowing control of polarization properties of the associated terahertz radiation.
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...
Efficiency at maximum power of a quantum heat engine based on two coupled oscillators.
Wang, Jianhui; Ye, Zhuolin; Lai, Yiming; Li, Weisheng; He, Jizhou
2015-06-01
We propose and theoretically investigate a system of two coupled harmonic oscillators as a heat engine. We show how these two coupled oscillators within undamped regime can be controlled to realize an Otto cycle that consists of two adiabatic and two isochoric processes. During the two isochores the harmonic system is embedded in two heat reservoirs at constant temperatures T(h) and T(c)(semigroup approach to model the thermal relaxation dynamics along the two isochoric processes, and we find the upper bound of efficiency at maximum power (EMP) η* to be a function of the Carnot efficiency η(C)(=1-T(c)/T(h)): η*≤η(+)≡η(C)(2)/[η(C)-(1-η(C))ln(1-η(C))], identical to those previously derived from ideal (noninteracting) microscopic, mesoscopic, and macroscopic systems.
Frequency-driven quantum oscillations in a graphene layer under circularly polarized ac fields
Energy Technology Data Exchange (ETDEWEB)
Vega Monroy, R., E-mail: ricardovega@mail.uniatlantico.edu.co; Martinez Castro, O.; Salazar Cohen, G.
2015-06-19
In this paper we predict a new type of quantum oscillations driven by the frequency of a circularly polarized ac field in a monolayer of graphene placed inside an optical cavity. We show that the displacement of the structure of photon-dressed electron states near the Fermi level and the electron transitions, from extended states to bound photon-dressed electron states inside an energy gap, lead to a periodic change of singularities in the electron density of states, resulting in quantum oscillations in thermodynamic, transport and other properties in graphene.
Interpreting Quantum Oscillation Experiments on Underdoped YBa2Cu3O6+x
Energy Technology Data Exchange (ETDEWEB)
Tranquada, J.M.
2010-02-01
On the basis of negative transport coefficients, it has been argued that the quantum oscillations observed in underdoped YBa{sub 2}Cu{sub 3}O{sub 6+x} in high magnetic fields must be due to antinodal electron pockets. We point out a counterexample in which electronlike transport in a hole-doped cuprate is associated with Fermi-arc states. We also present evidence that the antinodal gap in YBa{sub 2}Cu{sub 3}O{sub 6.67} is robust to modest applied magnetic fields. We suggest that these observations should be taken into account when interpreting the results of the quantum oscillation experiments.
Classical and Quantum Theory of Photothermal Cavity Cooling of a Mechanical Oscillator
Restrepo, Juan; Ciuti, Cristiano; Favero, Ivan
2010-01-01
Photothermal effects allow very efficient optomechanical coupling between mechanical degrees of freedom and photons. In the context of cavity cooling of a mechanical oscillator, the question of if the quantum ground state of the oscillator can be reached using photothermal back-action has been debated and remains an open question. Here we address this problem by complementary classical and quantum calculations. Both lead us to conclude that: first, the ground-state can indeed be reached using photothermal cavity cooling, second, it can be reached in a regime where the cavity detuning is small allowing a large amount of photons to enter the cavity.