Quantum entangling power of adiabatically connected Hamiltonians
International Nuclear Information System (INIS)
Hamma, Alioscia; Zanardi, Paolo
2004-01-01
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied
Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics
International Nuclear Information System (INIS)
Hoover, W.G.
1980-01-01
Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan
2018-02-01
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.
Geometry of quantal adiabatic evolution driven by a non-Hermitian Hamiltonian
International Nuclear Information System (INIS)
Wu Zhaoyan; Yu Ting; Zhou Hongwei
1994-01-01
It is shown by using a counter example, which is exactly solvable, that the quantal adiabatic theorem does not generally hold for a non-Hermitian driving Hamiltonian, even if it varies extremely slowly. The condition for the quantal adiabatic theorem to hold for non-Hermitian driving Hamiltonians is given. The adiabatic evolutions driven by a non-Hermitian Hamiltonian provide examples of a new geometric structure, that is the vector bundle in which the inner product of two parallelly transported vectors generally changes. A new geometric concept, the attenuation tensor, is naturally introduced to describe the decay or flourish of the open quantum system. It is constructed in terms of the spectral projector of the Hamiltonian. (orig.)
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
International Nuclear Information System (INIS)
Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery
2015-01-01
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Path-integral isomorphic Hamiltonian for including nuclear quantum effects in non-adiabatic dynamics
Tao, Xuecheng; Shushkov, Philip; Miller, Thomas F.
2018-03-01
We describe a path-integral approach for including nuclear quantum effects in non-adiabatic chemical dynamics simulations. For a general physical system with multiple electronic energy levels, a corresponding isomorphic Hamiltonian is introduced such that Boltzmann sampling of the isomorphic Hamiltonian with classical nuclear degrees of freedom yields the exact quantum Boltzmann distribution for the original physical system. In the limit of a single electronic energy level, the isomorphic Hamiltonian reduces to the familiar cases of either ring polymer molecular dynamics (RPMD) or centroid molecular dynamics Hamiltonians, depending on the implementation. An advantage of the isomorphic Hamiltonian is that it can easily be combined with existing mixed quantum-classical dynamics methods, such as surface hopping or Ehrenfest dynamics, to enable the simulation of electronically non-adiabatic processes with nuclear quantum effects. We present numerical applications of the isomorphic Hamiltonian to model two- and three-level systems, with encouraging results that include improvement upon a previously reported combination of RPMD with surface hopping in the deep-tunneling regime.
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Directory of Open Access Journals (Sweden)
Jeong Ryeol Choi
2015-01-01
Full Text Available An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
Topology hidden behind the breakdown of adiabaticity
International Nuclear Information System (INIS)
Fu, L.-B.; Chen, S.-G.
2005-01-01
For classical Hamiltonian systems, the adiabatic condition may fail at some critical points. However, the breakdown of the adiabatic condition does not always cause the adiabatic evolution to be destroyed. In this paper, we suggest a supplemental condition of the adiabatic evolution for the fixed points of classical Hamiltonian systems when the adiabatic condition breaks down at the critical points. As an example, we investigate the adiabatic evolution of the fixed points of a classical Hamiltonian system which has a number of applications
Transitionless driving on adiabatic search algorithm
Energy Technology Data Exchange (ETDEWEB)
Oh, Sangchul, E-mail: soh@qf.org.qa [Qatar Environment and Energy Research Institute, Qatar Foundation, Doha (Qatar); Kais, Sabre, E-mail: kais@purdue.edu [Qatar Environment and Energy Research Institute, Qatar Foundation, Doha (Qatar); Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States)
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
Hierarchical theory of quantum adiabatic evolution
International Nuclear Information System (INIS)
Zhang, Qi; Wu, Biao; Gong, Jiangbin
2014-01-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau–Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory. (paper)
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Coherent states of quantum systems. [Hamiltonians, variable magnetic field, adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Trifonov, D A
1975-01-01
Time-evolution of coherent states and uncertainty relations for quantum systems are considered as well as the relation between the various types of coherent states. The most general form of the Hamiltonians that keep the uncertainty products at a minimum is found using the coherent states. The minimum uncertainty packets are shown to be coherent states of the type nonstationary-system coherent states. Two specific systems, namely that of a generalized N-dimensional oscillator and that of a charged particle moving in a variable magnetic field, are treated as examples. The adiabatic approximation to the uncertainty products for these systems is also discussed and the minimality is found to be retained with an exponential accuracy.
International Nuclear Information System (INIS)
Chudnovsky, D.V.; Chudnovsky, G.V.
1980-01-01
We consider semi-classical approximation to factorized S-matrices. We show that this new class of matrices, called s-matrices, defines Hamiltonian structures for isospectral deformation equations. Concrete examples of factorized s-matrices are constructed and they are used to define Hamiltonian structure for general two-dimensional isospectral deformation systems. (orig.)
Studies in Chaotic adiabatic dynamics
International Nuclear Information System (INIS)
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)
Directory of Open Access Journals (Sweden)
J. D. Biamonte
2011-06-01
Full Text Available In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
Perturbative treatment of possible failures in the adiabatic theorem
International Nuclear Information System (INIS)
Vertesi, T.; Englman, R.
2005-01-01
Complete text of publication follows. The adiabatic theorem (AT) is one of the oldest and basic results in quantum physics, and has been in widespread use ever since. The theorem concerns the evolution of systems subject to slowly varying Hamiltonians. Roughly, its content is that a system prepared in an instantaneous eigenstate of a time-dependent Hamiltonian H(t) will remain close to an instantaneous eigenstate at later times, provided the Hamiltonian changes sufficiently slowly. The role of the AT in the study of slowly varying quantum mechanical systems spans a vast array of fields and applications. In a recent application the adiabatic geometric phases have been proposed to perform various quantum computational tasks on a naturally fault-tolerant way. Additional interest has arisen in adiabatic processes in connection with the concept of adiabatic quantum computing, where the solution to a problem is encoded in the (unknown) ground state of a (known) Hamiltonian. The evolution of the quantum state is governed by a time-dependent Hamiltonian H(t), starting with an initial Hamiltonian H i with a known ground state and slowly (adiabatically) evolving to the final Hamiltonian H f with the unknown ground state, e.g., H(t) = (1 - t/T )H i + (t/T )H f , (1) where 0 ≤ t/T ≤ 1 and T controls the rate at which H(t) varies. Since the ground state of the system is very robust against external perturbations and decoherence, this scheme offers many advantages compared to the conventional quantum circuit model of quantum computation. The achievable speed-up of adiabatic quantum algorithms (compared to classical methods) depends on the value of the run-time T. The standard AT yields a general criterion to estimate the necessary run-time T, however recently Marzlin and Sanders have claimed that an inconsistency does exist for a particular class of Hamiltonians, so that the condition for the estimate of T may do not hold. Marzlin and Sanders start with a time
Generalized shortcuts to adiabaticity and enhanced robustness against decoherence
Santos, Alan C.; Sarandy, Marcelo S.
2018-01-01
Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.
Modular Hamiltonians for deformed half-spaces and the averaged null energy condition
Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia
2016-09-01
We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on {{R}}^{1,d-1} . We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.
Hamiltonian term for a uniform dc electric field under the adiabatic approximation
Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee
2018-02-01
In this work, we show that the disorder-free Kubo formula for the nonequilibrium value of an observable due to a dc electric field, represented by Exx ̂ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-independent perturbation HMF. We derive the explicit expression for HMF and show that it originates from the adiabatic approximation to Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wave-packet formalism, we show that HMF reproduces the effect of the E field, i.e., Exx ̂ , up to the first order. This replacement suggests the emergence of a spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy-hole spin-3/2 Luttinger system.
Pulsed adiabatic structure and complete population transfer
International Nuclear Information System (INIS)
Shore, B.W.
1992-10-01
Population can be transferred between atomic or molecular energy states in a variety of ways. The basic idea of adiabatic transfer, discussed in many textbooks, is as follows. One begins with an atom that is in some single energy state (an eigenstate of an initial Hamiltonian). This energy state is one of many possible states, known variously as the unperturbed states or basis states or diabatic states. Next one begins to change the Hamiltonian very slowly. The changes may occur in either the diagonal elements (the basis state energies) or in the off-diagonal elements (interactions between basis states). If there are off-diagonal elements then the Hamiltonian will no longer commute with the original one. Because the Hamiltonian is no longer the one that was used to define the original basis states, it will cause these states to become mixed. However, if the change is sufficiently slow, the system can remain in a single eigenstate of the changing Hamiltonian -- an adiabatic state, composed of a combination of basis states. Finally, at some later time, one examines the system once again in the original basis. One finds that the population has undergone a change, and now resides in a different unperturbed state. One has produced population transfer. There are many illustrative examples of adiabatic passage, both theory and experiment. The author mentions briefly two common examples, inelastic collisions between atoms, and the static Stark effect in Rydberg atoms, before continuing with the main objective, a discussion of adiabatic passage induced by laser pulses
Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
International Nuclear Information System (INIS)
Lidar, Daniel A.; Rezakhani, Ali T.; Hamma, Alioscia
2009-01-01
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.
Berry phases for Landau Hamiltonians on deformed tori
Lévay, Péter
1995-06-01
Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γϑ (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γϑ the geodesic motion restricted to the fundamental domain of this group is chaotic.
Failure of geometric electromagnetism in the adiabatic vector Kepler problem
International Nuclear Information System (INIS)
Anglin, J.R.; Schmiedmayer, J.
2004-01-01
The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict the precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r 3 singularity which is an artifact of the adiabatic approximation
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1981-11-01
A Hamiltonian approach to plasma dynamics has numerous advantages over equivalent formulations which ignore the underlying Hamiltonian structure. In addition to achieving a deeper understanding of processes, Hamiltonian methods yield concise expressions (such as the Kubo form for linear susceptibility), greatly shorten the length of calculations, expose relationships (such as between the ponderomotive Hamiltonian and the linear susceptibility), determine invariants in terms of symmetry operations, and cover situations of great generality. In addition, they yield the Poincare invariants, in particular Liouville volume and adiabatic actions
Quantum-circuit model of Hamiltonian search algorithms
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
We analyze three different quantum search algorithms, namely, the traditional circuit-based Grover's algorithm, its continuous-time analog by Hamiltonian evolution, and the quantum search by local adiabatic evolution. We show that these algorithms are closely related in the sense that they all perform a rotation, at a constant angular velocity, from a uniform superposition of all states to the solution state. This makes it possible to implement the two Hamiltonian-evolution algorithms on a conventional quantum circuit, while keeping the quadratic speedup of Grover's original algorithm. It also clarifies the link between the adiabatic search algorithm and Grover's algorithm
Connection between optimal control theory and adiabatic-passage techniques in quantum systems
Assémat, E.; Sugny, D.
2012-08-01
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from Pontryagin's maximum principle. In a three-level quantum system, we show that the stimulated Raman adiabatic passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.
Hamiltonian closures in fluid models for plasmas
Tassi, Emanuele
2017-11-01
This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and
Magnus approximation in the adiabatic picture
International Nuclear Information System (INIS)
Klarsfeld, S.; Oteo, J.A.
1991-01-01
A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs
Dynamical constraints and adiabatic invariants in chemical reactions.
Lorquet, J C
2007-08-23
For long-range electrostatic potentials and, more generally, when the topography of the potential energy surface is locally simple, the reaction path coordinate is adiabatically separable from the perpendicular degrees of freedom. For the ion-permanent dipole and ion-quadrupole interactions, the Poisson bracket of the adiabatic invariant decreases with the interfragment distance more rapidly than the electrostatic potential. The smaller the translational momentum, the moment of inertia of the neutral fragment, and the dipole or quadrupole moments are, the more reliable the adiabatic approximation is, as expected from the usual argumentation. Closed-form expressions for an effective one-dimensional potential in an adiabatic Hamiltonian are given. Connection with a model where the decoupling is exact is obtained in the limit of an infinitely heavy dipole. The dynamics is also constrained by adiabatic invariance for a harmonic valley about a curved reaction path, as shown by the reaction path Hamiltonian method. The maximum entropy method reveals that, as a result of the invariance properties of the entropy, constraints whose validity has been demonstrated locally only subsist in all parts of phase space. However, their form varies continuously, and they are not necessarily expressed in simple terms as they are in the asymptotic region. Therefore, although the influence of adiabatic invariance has been demonstrated at asymptotically large values of the reaction coordinate only, it persists in more interesting ranges.
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-09
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Directory of Open Access Journals (Sweden)
Dave Bacon
2013-06-01
Full Text Available We describe a many-body quantum system that can be made to quantum compute by the adiabatic application of a large applied field to the system. Prior to the application of the field, quantum information is localized on one boundary of the device, and after the application of the field, this information propagates to the other side of the device, with a quantum circuit applied to the information. The applied circuit depends on the many-body Hamiltonian of the material, and the computation takes place in a degenerate ground space with symmetry-protected topological order. Such “adiabatic quantum transistors” are universal adiabatic quantum computing devices that have the added benefit of being modular. Here, we describe this model, provide arguments for why it is an efficient model of quantum computing, and examine these many-body systems in the presence of a noisy environment.
Optimal protocols for Hamiltonian and Schrödinger dynamics
International Nuclear Information System (INIS)
Schmiedl, Tim; Dieterich, Eckhard; Dieterich, Peter-Simon; Seifert, Udo
2009-01-01
For systems in an externally controllable time dependent potential, the optimal protocol minimizes the mean work spent in a finite time transition between given initial and final values of a control parameter. For an initially thermalized ensemble, we consider both Hamiltonian evolution for classical systems and Schrödinger evolution for quantum systems. In both cases, we show that for harmonic potentials, the optimal work is given by the adiabatic work even in the limit of short transition times. This result is counter-intuitive because the adiabatic work is substantially smaller than the work for an instantaneous jump. We also perform numerical calculations for the optimal protocol for Hamiltonian dynamics in an anharmonic quartic potential. For a two-level spin system, we give examples where the adiabatic work can be reached in either a finite or an arbitrarily short transition time depending on the allowed parameter space
Superconducting system for adiabatic quantum computing
Energy Technology Data Exchange (ETDEWEB)
Corato, V [Dipartimento di Ingegneria dell' Informazione, Second University of Naples, 81031 Aversa (Italy); Roscilde, T [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484 (Canada); Ruggiero, B [Istituto di Cibernetica ' E.Caianiello' del CNR, I-80078, Pozzuoli (Italy); Granata, C [Istituto di Cibernetica ' E.Caianiello' del CNR, I-80078, Pozzuoli (Italy); Silvestrini, P [Dipartimento di Ingegneria dell' Informazione, Second University of Naples, 81031 Aversa (Italy)
2006-06-01
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results.
The group of Hamiltonian automorphisms of a star product
La Fuente-Gravy, Laurent
2015-01-01
We deform the group of Hamiltonian diffeomorphisms into the group of Hamiltonian automorphisms of a formal star product on a symplectic manifold. We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
The Group of Hamiltonian Automorphisms of a Star Product
Energy Technology Data Exchange (ETDEWEB)
La Fuente-Gravy, Laurent, E-mail: lfuente@ulg.ac.be [Université de Liège, Département de Mathématique (Belgium)
2016-09-15
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
The Group of Hamiltonian Automorphisms of a Star Product
International Nuclear Information System (INIS)
La Fuente-Gravy, Laurent
2016-01-01
We deform the group of Hamiltonian diffeomorphisms into a group of Hamiltonian automorphisms, Ham(M,∗), of a formal star product ∗ on a symplectic manifold (M,ω). We study the geometry of that group and deform the Flux morphism in the framework of deformation quantization.
Normal form for mirror machine Hamiltonians
International Nuclear Information System (INIS)
Dragt, A.J.; Finn, J.M.
1979-01-01
A systematic algorithm is developed for performing canonical transformations on Hamiltonians which govern particle motion in magnetic mirror machines. These transformations are performed in such a way that the new Hamiltonian has a particularly simple normal form. From this form it is possible to compute analytic expressions for gyro and bounce frequencies. In addition, it is possible to obtain arbitrarily high order terms in the adiabatic magnetic moment expansion. The algorithm makes use of Lie series, is an extension of Birkhoff's normal form method, and has been explicitly implemented by a digital computer programmed to perform the required algebraic manipulations. Application is made to particle motion in a magnetic dipole field and to a simple mirror system. Bounce frequencies and locations of periodic orbits are obtained and compared with numerical computations. Both mirror systems are shown to be insoluble, i.e., trajectories are not confined to analytic hypersurfaces, there is no analytic third integral of motion, and the adiabatic magnetic moment expansion is divergent. It is expected also that the normal form procedure will prove useful in the study of island structure and separatrices associated with periodic orbits, and should facilitate studies of breakdown of adiabaticity and the onset of ''stochastic'' behavior
Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist
International Nuclear Information System (INIS)
Castro, P.G.; Kullock, R.; Toppan, F.
2011-01-01
Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)
Random matrix model of adiabatic quantum computing
International Nuclear Information System (INIS)
Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2005-01-01
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size
Dissipation in adiabatic quantum computers: lessons from an exactly solvable model
Keck, Maximilian; Montangero, Simone; Santoro, Giuseppe E.; Fazio, Rosario; Rossini, Davide
2017-11-01
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-product-operator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.
Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist
Energy Technology Data Exchange (ETDEWEB)
Castro, P.G., E-mail: pgcastro@cbpf.b [Universidade Federal de Juiz de Fora (DM/ICE/UFJF), Juiz de Fora, MG (Brazil). Inst. de Ciencias Exatas. Dept. de Matematica; Kullock, R.; Toppan, F., E-mail: ricardokl@cbpf.b, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (TEO/CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Fisica Teorica
2011-07-01
Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)
Adiabatic evolution of decoherence-free subspaces and its shortcuts
Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.
2017-10-01
The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.
Relativistic magnetohydrodynamics as a Hamiltonian system
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, A.
1985-01-01
The equations of ideal relativistic magnetohydrodynamics in the laboratory frame form a noncanonical Hamiltonian system with the same Poisson bracket as for the nonrelativistic system, but with dynamical variables and Hamiltonian obtained via a regular deformation of their nonrelativistic counterparts [fr
Adiabatic rotation, quantum search, and preparation of superposition states
International Nuclear Information System (INIS)
Siu, M. Stewart
2007-01-01
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied 'straight line' adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev's toric code state, the cluster state of the measurement-based computation model, and the history state used in the adiabatic simulation of a quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the standard adiabatic algorithm
Adiabatically steered open quantum systems: Master equation and optimal phase
International Nuclear Information System (INIS)
Salmilehto, J.; Solinas, P.; Ankerhold, J.; Moettoenen, M.
2010-01-01
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a nonsteered system in the first superadiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
Shortcuts to adiabaticity in cutting a spin chain
Energy Technology Data Exchange (ETDEWEB)
Ren, Feng-Hua [Department of Physics, Ocean University of China, Qingdao 266100 (China); School of Computer Engineering, Qingdao Technological University, Qingdao 266033 (China); Wang, Zhao-Ming, E-mail: mingmoon78@126.com [Department of Physics, Ocean University of China, Qingdao 266100 (China); Gu, Yong-Jian, E-mail: yjgu@ouc.edu.cn [Department of Physics, Ocean University of China, Qingdao 266100 (China)
2017-01-15
“Shortcuts to adiabaticity” represents a strategy for accelerating a quantum adiabatic process, is useful for preparing or manipulating a quantum state. In this paper, we investigate the adiabaticity in the dynamics of an XY spin chain. During the process of cutting one long chain into two short chains, a “shortcut” can be obtained by applying a sequence of external pulses. The fidelity which measures the adiabaticity can be dramatically enhanced by increasing the pulse strength or pulse duration time. This reliability can be kept for different types of pulses, such as random pulse time interval or random strength. The free choice of the pulse can be explained by the adiabatic representation of the Hamiltonian, and it shows that the control effects are determined by the integral of the control function in the time domain. - Highlights: • “Shortcuts to adiabaticity” is proposed by applying external pulses. • The adiabaticity can be accelerated by increasing pulse strength or duration time. • Control effects are determined by the integral of the control function with respect to time.
On the adiabatic theorem when eigenvalues dive into the continuum
DEFF Research Database (Denmark)
Cornean, Decebal Horia; Jensen, Arne; Knörr, Hans Konrad
2018-01-01
We consider a reduced two-channel model of an atom consisting of a quantum dot coupled to an open scattering channel described by a three-dimensional Laplacian. We are interested in the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial...... in the adiabatic limit. At the end of the paper, we present a short outlook on how our method may be extended to cover other classes of Hamiltonians; details will be given elsewhere....
Adiabatic graph-state quantum computation
International Nuclear Information System (INIS)
Antonio, B; Anders, J; Markham, D
2014-01-01
Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any MBQC on a graph state with generalized flow (gflow) can be converted into an adiabatically driven holonomic computation, which we call adiabatic graph-state quantum computation (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of H-dot as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated. (paper)
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Piepenbring, R.
1978-01-01
Matrix elements of a general Hamiltonian H in a subspace spanned by collective K/sup π/+ deformed phonons are derived with the help of recursion formulas. Various approximations are discussed both in the fermion space and in the boson space. Careful comparisons are made in the framework of a simple solvable model
Chen, Ye-Hong; Xia, Yan; Song, Jie; Chen, Qing-Qin
2015-10-28
Berry's approach on "transitionless quantum driving" shows how to set a Hamiltonian which drives the dynamics of a system along instantaneous eigenstates of a reference Hamiltonian to reproduce the same final result of an adiabatic process in a shorter time. In this paper, motivated by transitionless quantum driving, we construct shortcuts to adiabatic passage in a three-atom system to create the Greenberger-Horne-Zeilinger states with the help of quantum Zeno dynamics and of non-resonant lasers. The influence of various decoherence processes is discussed by numerical simulation and the result proves that the scheme is fast and robust against decoherence and operational imperfection.
Albash, Tameem; Lidar, Daniel A.
2018-01-01
Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.
Reaction Hamiltonian and state-to-state description of chemical reactions
International Nuclear Information System (INIS)
Ruf, B.A.; Kresin, V.Z.; Lester, W.A. Jr.
1985-08-01
A chemical reaction is treated as a quantum transition from reactants to products. A specific reaction Hamiltonian (in second quantization formalism) is introduced. The approach leads to Franck-Condon-like factor, and adiabatic method in the framework of the nuclear motion problems. The influence of reagent vibrational state on the product energy distribution has been studied following the reaction Hamiltonian method. Two different cases (fixed available energy and fixed translational energy) are distinguished. Results for several biomolecular reactions are presented. 40 refs., 5 figs
Experimental study on the adiabatic shear bands
International Nuclear Information System (INIS)
Affouard, J.
1984-07-01
Four martensitic steels (Z50CDV5 steel, 28CND8 steel, 35NCDV16 steel and 4340 steel) with different hardness between 190 and 600 Hsub(B) (Brinell hardness), have been studied by means of dynamic compressive tests on split Hopkinson pressure bar. Microscopic observations show that the fracture are associated to the development of adiabatic shear bands (except 4340 steel with 190 Hsub(B) hardness). By means of tests for which the deformation is stopped at predetermined levels, the measurement of shear and hardness inside the band and the matrix indicates the chronology of this phenomenon: first the localization of shear, followed by the formation of adiabatic shear band and ultimatly crack initiation and propagation. These results correlated with few simulations by finite elements have permitted to suggest two mecanisms of deformation leading to the formation of adiabatic shear bands in this specific test [fr
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Change of adiabatic invariant near the separatrix
International Nuclear Information System (INIS)
Bulanov, S.V.
1995-10-01
The properties of particle motion in the vicinity of the separatrix in a phase plane are investigated. The change of adiabatic invariant value due to the separatrix crossing is evaluated as a function of a perturbation parameter magnitude and a phase of a particle for time dependent Hamiltonians. It is demonstrated that the change of adiabatic invariant value near the separatrix birth is much larger than that in the case of the separatrix crossing near the saddle point in a phase plane. The conditions of a stochastic regime to appear around the separatrix are found. The results are applied to study the longitudinal invariant behaviour of charged particles near singular lines of the magnetic field. (author). 22 refs, 9 figs
Non-stoquastic Hamiltonians in quantum annealing via geometric phases
Vinci, Walter; Lidar, Daniel A.
2017-09-01
We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.
Nonlinearly deformed W∞ algebra and second hamiltonian structure of KP hierarchy
International Nuclear Information System (INIS)
Yu Feng; Wu Yongshi
1992-01-01
The characteristic nonlinearity of W N algebras, appropriate for their many applications in two-dimensional quantum physics, is lost in the usual large-N limits. In this paper we search for nonlinear extensions of the Virasoro algebra that incorporate all higher-spin currents with spin s≥2. We show that under certain natural homogeneity requirements, the Jacobi identities lead to a unique nonlinear, centerless deformation of classical w ∞ and W ∞ . The latter, which we call dW/dt ∞ , constitutes a universal W-algebra which is very likely to contain all W N algebras by reduction. Also it is closely related to the linear W 1+∞ by a set of interesting recursion relations, which suggests the isomorphism of dW/dt ∞ to the second hamiltonian structure of the KP hierarchy proposed by Dickey. The implications for the symmetries in two-dimensional quantum gravity and noncritical c≤1 strings in the context of the KP approach are discussed. (orig.)
Two-component feedback loops and deformed mechanics
International Nuclear Information System (INIS)
Tourigny, David S.
2015-01-01
It is shown that a general two-component feedback loop can be viewed as a deformed Hamiltonian system. Some of the implications of using ideas from theoretical physics to study biological processes are discussed. - Highlights: • Two-component molecular feedback loops are viewed as q-deformed Hamiltonian systems. • Deformations are reversed using Jackson derivatives to take advantage of working in the Hamiltonian limit. • New results are derived for the particular examples considered. • General deformations are suggested to be associated with a broader class of biological processes
Adiabatic theory of nonlinear electron cyclotron resonance heating
International Nuclear Information System (INIS)
Kotel'nikov, I.A.; Stupakov, G.V.
1989-01-01
Plasma heating at electron frequency by an ordinary wave propagating at right angle to unidirectional magnetic field is treated. Injected microwave power is assumed to be so large that relativistic change of electron gyrofrequency during one flight thorugh the wave beam is much greater than inverse time of flight. The electron motion in the wave field is described using Hamiltonian formalism in adiabatic approximation. It is shown that energy coupling from the wave to electrons is due to a bifurcation of electron trajectory which results in a jumpm of the adiabatic invariant. The probability of bifurcational transition from one trajectory to another is calculated analytically and is used for the estimation of the beam power absorbed in plasma. 6 refs.; 2 figs
Adiabatic condition and the quantum hitting time of Markov chains
International Nuclear Information System (INIS)
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-01-01
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P ' where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP ' and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
Quantum Adiabatic Algorithms and Large Spin Tunnelling
Boulatov, A.; Smelyanskiy, V. N.
2003-01-01
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Adiabatic quantum computing with spin qubits hosted by molecules.
Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji
2015-01-28
A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.
Energy Technology Data Exchange (ETDEWEB)
Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr [Center for Self-assembly and Complexity, Institute for Basic Science (IBS), Pohang 790-784 (Korea, Republic of); Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784 (Korea, Republic of)
2014-04-28
Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.
Sdg interacting boson hamiltonian in the seniority scheme
Energy Technology Data Exchange (ETDEWEB)
Yoshinaga, N.
1989-03-06
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagnoalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
sdg Interacting boson hamiltonian in the seniority scheme
Yoshinaga, N.
1989-03-01
The sdg interacting boson hamiltonian is derived in the seniority scheme. We use the method of Otsuka, Arima and Iachello in order to derive the boson hamiltonian from the fermion hamiltonian. To examine how good is the boson approximation in the zeroth-order, we carry out the exact shell model calculations in a single j-shell. It is found that almost all low-lying levels are reproduced quite well by diagonalizing the sdg interacting boson hamiltonian in the vibrational case. In the deformed case the introduction of g-bosons improves the reproduction of the spectra and of the binding energies which are obtained by diagonalizing the exact shell model hamiltonian. In particular the sdg interacting boson model reproduces well-developed rotational bands.
Integrable Hamiltonian systems and spectral theory
Moser, J
1981-01-01
Classical integrable Hamiltonian systems and isospectral deformations ; geodesics on an ellipsoid and the mechanical system of C. Neumann ; the Schrödinger equation for almost periodic potentials ; finite band potentials ; limit cases, Bargmann potentials.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
An introduction to the adiabatic time-dependent Hartree-Fock method
International Nuclear Information System (INIS)
Giannoni, M.J.
1984-05-01
The aim of the adiabatic time-dependent Hartree-Fock method is to investigate the microscopic foundations of the phenomenological collective models. We briefly review the general formulation, which consists in deriving a Bohr-like Hamiltonian from a mean field theory, and discuss the limiting case where only a few collective variables participate to the motion. Some applications to soft nuclei and heavy ion collisions are presented
Phase avalanches in near-adiabatic evolutions
International Nuclear Information System (INIS)
Vertesi, T.; Englman, R.
2006-01-01
In the course of slow, nearly adiabatic motion of a system, relative changes in the slowness can cause abrupt and high magnitude phase changes, ''phase avalanches,'' superimposed on the ordinary geometric phases. The generality of this effect is examined for arbitrary Hamiltonians and multicomponent (>2) wave packets and is found to be connected (through the Blaschke term in the theory of analytic signals) to amplitude zeros in the lower half of the complex time plane. Motion on a nonmaximal circle on the Poincare-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes
Theory of collective Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Zhang Qingying
1982-02-01
Starting from the cranking model, we derive the nuclear collective Hamiltonian. We expand the total energy of the collective motion of the ground state of even--even nuclei in powers of the deformation parameter ..beta... In the first approximation, we only take the lowest-order non-vanished terms in the expansion. The collective Hamiltonian thus obtained rather differs from the A. Bohr's Hamiltonian obtained by the irrotational incompressible liquid drop model. If we neglect the coupling term between ..beta..-and ..gamma..-vibration, our Hamiltonian then has the same form as that of A. Bohr. But there is a difference between these collective parameters. Our collective parameters are determined by the state of motion of the nucleous in the nuclei. They are the microscopic expressions. On the contrary, A. Bohr's collective parameters are only the simple functions of the microscopic physical quantities (such as nuclear radius and surface tension, etc.), and independent of the state of motion of the nucleons in the nuclei. Furthermore, there exist the coupling term between ..beta..-and ..gamma..-vibration and the higher-order terms in our expansion. They can be treated as the perturbations. There are no such terms in A. Bohr's Hamiltonian. These perturbation terms will influence the rotational, vibrational spectra and the ..gamma..-transition process, etc.
International Nuclear Information System (INIS)
Figueroa-O'Farrill, J.M.; Mas, J.; Ramos, E.
1993-01-01
The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting W-algebra is a one-parameter deformation of W KP admitting a central extension for generic values of the parameter, reducing naturally to W n for special values of the parameter, and contracting to the centrally extended W 1+∞ , W ∞ and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to W KP . The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of W ∞ which contracts to a new nonlinear algebra of the W ∞ -type. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Li Xunjun; Dudek, J.; Romain, P. (Centre de Recherches Nucleaires, IN2P3-CNRS, Univ. Louis Pasteur, 67 - Strasbourg (France))
1991-11-21
Symmetry properties of the general average-field hamiltonian-matrix resulting from the geometrical symmetries of the hamiltonian itself are derived and discussed. The corresponding numerical algorithms are constructed. Total energy calculations for superdeformed nuclei are then extended to include the usually neglected deformation modes {alpha}{sub {lambda}=3{mu}{ne}0} in the expansion of the nuclear surface expression R({theta}, {phi}; {l brace}{alpha}{r brace})=c({l brace}{alpha}{r brace})R{sub 0}(1+{Sigma}{sub {lambda}} {Sigma}{sub {mu}=-{lambda}}{sup {lambda}} {alpha}{sub {lambda}{mu}}{sup *}{Upsilon}{sub {lambda}{mu}}({theta}, {phi})). The general trends in the shell-energy dependence on {alpha}{sub {lambda}=3{mu}} and the implied instabilities in the superdeformed configurations of the rare earth nuclei are studied using the Strutinsky formula with the macroscopic part taken in the form of the folded-Yukawa plus exponential interaction. A possibility of new (double superdeformed minimum) structures coexisting in some nuclei and resulting from the proton shell effects is predicted and illustrated. No significant neutron effects are found in the rare earth superdeformed nuclei considered. (orig.).
Energy Technology Data Exchange (ETDEWEB)
Zhan, Hongyi, E-mail: h.zhan@uq.edu.au [Centre for Advanced Materials Processing and Manufacture, School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, Queensland 4072 (Australia); Zeng, Weidong [State Key Laboratory of Solidification Processing, School of Materials, Northwestern Polytechnical University, Xi' an 710072 (China); Wang, Gui [Centre for Advanced Materials Processing and Manufacture, School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, Queensland 4072 (Australia); Defence Material Technology Centre, Level 2, 24 Wakefield St, Hawthorn, VIC 3122 (Australia); Kent, Damon [School of Science and Engineering, University of the Sunshine Coast, Sippy Downs, Queensland 4575 (Australia); Dargusch, Matthew [Centre for Advanced Materials Processing and Manufacture, School of Mechanical and Mining Engineering, The University of Queensland, St Lucia, Queensland 4072 (Australia); Defence Material Technology Centre, Level 2, 24 Wakefield St, Hawthorn, VIC 3122 (Australia)
2015-04-15
The microstructural evolution and grain refinement within adiabatic shear bands in the Ti6554 alloy deformed at high strain rates and elevated temperatures have been characterized using transmission electron microscopy. No stress drops were observed in the corresponding stress–strain curve, indicating that the initiation of adiabatic shear bands does not lead to the loss of load capacity for the Ti6554 alloy. The outer region of the shear bands mainly consists of cell structures bounded by dislocation clusters. Equiaxed subgrains in the core area of the shear band can be evolved from the subdivision of cell structures or reconstruction and transverse segmentation of dislocation clusters. It is proposed that dislocation activity dominates the grain refinement process. The rotational recrystallization mechanism may operate as the kinetic requirements for it are fulfilled. The coexistence of different substructures across the shear bands implies that the microstructural evolution inside the shear bands is not homogeneous and different grain refinement mechanisms may operate simultaneously to refine the structure. - Graphical abstract: Display Omitted - Highlights: • The microstructure within the adiabatic shear band was characterized by TEM. • No stress drops were observed in the corresponding stress–strain curve. • Dislocation activity dominated the grain refinement process. • The kinetic requirements for rotational recrystallization mechanism were fulfilled. • Different grain refinement mechanisms operated simultaneously to refine the structure.
Optimization using quantum mechanics: quantum annealing through adiabatic evolution
International Nuclear Information System (INIS)
Santoro, Giuseppe E; Tosatti, Erio
2006-01-01
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'ℎ' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models-double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schroedinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau-Zener tunnelling phenomena is discussed and emphasized. (topical review)
η Condensate of Fermionic Atom Pairs via Adiabatic State Preparation
International Nuclear Information System (INIS)
Kantian, A.; Daley, A. J.; Zoller, P.
2010-01-01
We discuss how an η condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalization group methods, we analyze a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
Adiabatic shear behaviors in rolled and annealed pure titanium subjected to dynamic impact loading
Energy Technology Data Exchange (ETDEWEB)
Kuang, Lianjun; Chen, Zhiyong, E-mail: czysh@netease.com; Jiang, Yanghui; Wang, Zhiming; Wang, Renke; Liu, Chuming
2017-02-08
The hat-shaped samples cut from rolled and annealed titanium plates were prepared to explore the adiabatic shear behaviors subjected to high-strain-rate deformation operated via Split Hopkinson Pressure Bar. The dynamic shear response calculation reveals that dynamic deformation processes of both state samples can be divided in similar three stages but rolled sample shows a higher susceptibility of adiabatic shear localization compared with the annealed one. Optical microscopy and electronic backscatter diffraction technique (EBSD) were used to systematically analyze the microstructure and texture characteristics. The results show that adiabatic shear bands form in both state samples and rotational dynamic recrystallization (RDRX) occurs within shear area and results in the formation of ultrafine equiaxed grains. Furthermore, ultrafine equiaxed grains within adiabatic shear bands have the same texture feature that <11–20> direction and {10-10} plane parallel to macro local shear direction and shear plane respectively. In the deformation region around the shear band, {10–12} <–1011> tensile and {11–22} <11-2-3> compressive two types twins are observed in both state samples and {10–12} <–1011> tensile twins are more frequently observed in rolled sample. In the rolled sample, {10–12} <–1011> tensile twins are more likely to happen in the hat-brim side than the hat-body side due to the difference of stress state in two sides.
Modification of optical properties by adiabatic shifting of resonances in a four-level atom
Dutta, Bibhas Kumar; Panchadhyayee, Pradipta
2018-04-01
We describe the linear and nonlinear optical properties of a four-level atomic system, after reducing it to an effective two-level atomic model under the condition of adiabatic shifting of resonances driven by two coherent off-resonant fields. The reduced form of the Hamiltonian corresponding to the two-level system is obtained by employing an adiabatic elimination procedure in the rate equations of the probability amplitudes for the proposed four-level model. For a weak probe field operating in the system, the nonlinear dependence of complex susceptibility on the Rabi frequencies and the detuning parameters of the off-resonant driving fields makes it possible to exhibit coherent control of single-photon and two-photon absorption and transparency, the evolution of enhanced Self-Kerr nonlinearity and noticeable dispersive switching. We have shown how the quantum interference results in the generic four-level model at the adiabatic limit. The present scheme describes the appearance of single-photon transparency without invoking any exact two-photon resonance.
Hamiltonian reductions in plasma physics about intrinsic gyrokinetic
International Nuclear Information System (INIS)
Guillebon de Resnes, L. de
2013-01-01
Gyrokinetic is a key model for plasma micro-turbulence, commonly used for fusion plasmas or small-scale astrophysical turbulence, for instance. The model still suffers from several issues, which could imply to reconsider the equations. This thesis dissertation clarifies three of them. First, one of the coordinates caused questions, both from a physical and from a mathematical point of view; a suitable constrained coordinate is introduced, which removes the issues from the theory and explains the intrinsic structures underlying the questions. Second, the perturbative coordinate transformation for gyrokinetic was computed only at lowest orders; explicit induction relations are obtained to go arbitrary order in the expansion. Third, the introduction of the coupling between the plasma and the electromagnetic field was not completely satisfactory; using the Hamiltonian structure of the dynamics, it is implemented in a more appropriate way, with strong consequences on the gyrokinetic equations, especially about their Hamiltonian structure. In order to address these three main points, several other results are obtained, for instance about the origin of the guiding-center adiabatic invariant, about a very efficient minimal guiding center transformation, or about an intermediate Hamiltonian model between Vlasov-Maxwell and gyrokinetic, where the characteristics include both the slow guiding-center dynamics and the fast gyro-angle dynamics. In addition, various reduction methods are used, introduced or developed, e.g. a Lie-transform of the equations of motion, a lifting method to transfer particle reductions to the corresponding Hamiltonian field dynamics, or a truncation method related both to Dirac's theory of constraints and to a projection onto a Lie-subalgebra. Besides gyrokinetic, this is useful to clarify other Hamiltonian reductions in plasma physics, for instance for incompressible or electrostatic dynamics, for magnetohydrodynamics, or for fluid closures including
Hamiltonian dynamics of extended objects
Capovilla, R.; Guven, J.; Rojas, E.
2004-12-01
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.
Hamiltonian dynamics of extended objects
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2004-01-01
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations
Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle
International Nuclear Information System (INIS)
Brink, D.M.; Giannoni, M.J.; Veneroni, M.
1975-10-01
A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamilton's principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinated and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics [fr
Adiabatic perturbation theory for atoms and molecules in the low-frequency regime.
Martiskainen, Hanna; Moiseyev, Nimrod
2017-12-14
There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when iℏω∂∂τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).
RG-Whitham dynamics and complex Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Gorsky
2015-06-01
Full Text Available Inspired by the Seiberg–Witten exact solution, we consider some aspects of the Hamiltonian dynamics with the complexified phase space focusing at the renormalization group (RG-like Whitham behavior. We show that at the Argyres–Douglas (AD point the number of degrees of freedom in Hamiltonian system effectively reduces and argue that anomalous dimensions at AD point coincide with the Berry indexes in classical mechanics. In the framework of Whitham dynamics AD point turns out to be a fixed point. We demonstrate that recently discovered Dunne–Ünsal relation in quantum mechanics relevant for the exact quantization condition exactly coincides with the Whitham equation of motion in the Ω-deformed theory.
Hamiltonian dynamics of extended objects
Energy Technology Data Exchange (ETDEWEB)
Capovilla, R [Departamento de FIsica, Centro de Investigacion y de Estudios Avanzados del IPN, Apdo Postal 14-740, 07000 Mexico, DF (Mexico); Guven, J [School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4 (Ireland); Rojas, E [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apdo Postal 70-543, 04510 Mexico, DF (Mexico)
2004-12-07
We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler-Lagrange equations.
Hamiltonian PDEs and Frobenius manifolds
International Nuclear Information System (INIS)
Dubrovin, Boris A
2008-01-01
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
Hamiltonian PDEs and Frobenius manifolds
Energy Technology Data Exchange (ETDEWEB)
Dubrovin, Boris A [Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
2008-12-31
In the first part of this paper the theory of Frobenius manifolds is applied to the problem of classification of Hamiltonian systems of partial differential equations depending on a small parameter. Also developed is a deformation theory of integrable hierarchies including the subclass of integrable hierarchies of topological type. Many well-known examples of integrable hierarchies, such as the Korteweg-de Vries, non-linear Schroedinger, Toda, Boussinesq equations, and so on, belong to this subclass that also contains new integrable hierarchies. Some of these new integrable hierarchies may be important for applications. Properties of the solutions to these equations are studied in the second part. Consideration is given to the comparative study of the local properties of perturbed and unperturbed solutions near a point of gradient catastrophe. A Universality Conjecture is formulated describing the various types of critical behaviour of solutions to perturbed Hamiltonian systems near the point of gradient catastrophe of the unperturbed solution.
arXiv Lightcone Effective Hamiltonians and RG Flows
Fitzpatrick, A. Liam; Katz, Emanuel; Vitale, Lorenzo G.; Walters, Matthew T.
We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.
Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature
Directory of Open Access Journals (Sweden)
Orlando Ragnisco
2007-02-01
Full Text Available An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3 integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.
Hamiltonian aspects of three-wave resonant interactions in gas dynamics
Webb, G. M.; Zakharian, A.; Brio, M.; Zank, G. P.
1997-06-01
Equations describing three-wave resonant interactions in adiabatic gas dynamics in one Cartesian space dimension derived by Majda and Rosales are expressed in terms of Lagrangian and Hamiltonian variational principles. The equations consist of two coupled integro-differential Burgers equations for the backward and forward sound waves that are coupled by integral terms that describe the resonant reflection of a sound wave off an entropy wave disturbance to produce a reverse sound wave. Similarity solutions and conservation laws for the equations are derived using symmetry group methods for the special case where the entropy disturbance consists of a periodic saw-tooth profile. The solutions are used to illustrate the interplay between the nonlinearity represented by the Burgers self-wave interaction terms and wave dispersion represented by the three-wave resonant interaction terms. Hamiltonian equations in Fourier (p,t) space are also obtained where p is the Fourier space variable corresponding to the fast phase variable 0305-4470/30/12/013/img6 of the waves. The latter equations are transformed to normal form in order to isolate the normal modes of the system.
Fast fracture: an adiabatic restriction on thermally activated crack propagation
Energy Technology Data Exchange (ETDEWEB)
Burns, S.J.
1978-01-01
Slow, isothermal, crack propagation is widely suspected to be rate controlled by thermally activated plastic deformation in the crack tip region. Adiabatic conditions are generally established in the fracture modified material at the tip of a crack during fast fracture. The temperature of this material is not the temperature of the specimen and is generally not measured during fast fracture. Thus, a complete thermodynamic description of adiabatic crack propagation data can not be made. When the slow, isothermal, crack propagation mechanisms are assumed to be operative during adiabatic crack propagation then certain predictions can be made. For example: the changes in the driving force due to temperature and rate are always in the opposite sense; there is no minimum in the driving force versus crack velocity without a change in mechanism; the temperature rise in the crack tip fracture modified material is determined mainly by the activation enthalpy for crack propagation; the interpretation of fast fracture structural steel data from simple plastic models is suspect since these materials have dissimilar isothermal temperature dependencies.
A position-dependent mass harmonic oscillator and deformed space
da Costa, Bruno G.; Borges, Ernesto P.
2018-04-01
We consider canonically conjugated generalized space and linear momentum operators x^ q and p^ q in quantum mechanics, associated with a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q. A canonical transformation (x ^ ,p ^ ) →(x^ q,p^ q ) leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space (x, p) may be expressed in terms of the deformed (dual) q-derivative. We revisit the problem of a q-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces (x, p) and (xq, pq) are analyzed for different values of the deformation parameter. Finally, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.
Sine-square deformation of solvable spin chains and conformal field theories
International Nuclear Information System (INIS)
Katsura, Hosho
2012-01-01
We study solvable spin chains, one-dimensional massless Dirac fermions and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the function f(x) = sin 2 (πx/ℓ), where x is the position and ℓ is the length of the system. For the XY chain and the transverse field Ising chain at criticality, it is shown that the ground state of an open system with SSD is identical to that of a uniform chain with periodic boundary conditions. The same holds for the massless Dirac fermions with SSD, corresponding to the continuum limit of the gapless XY chain. For general CFTs, we find that the Hamiltonian of a system with SSD has an expression in terms of the generators of the Virasoro algebra. This allows us to show that the vacuum state is an exact eigenstate of the sine-square deformed Hamiltonian. Furthermore, for a restricted class of CFTs associated with affine Lie (Kac–Moody) algebras, including c = 1 Gaussian CFT, we prove that the vacuum is an exact ground state of the deformed Hamiltonian. This explains why the SSD has succeeded in suppressing boundary effects in one-dimensional critical systems, as observed in previous numerical studies. (paper)
Deformed model Sp(4) model for studying pairing correlations in atomic nuclei
Georgieva, A I; Sviratcheva, K
2002-01-01
A fermion representation of the compact symplectic sp(4) algebra introduces a theoretical framework for describing pairing correlations in atomic nuclei. The important non-deformed and deformed subalgebras of sp sub ( sub q sub ) (4) and the corresponding reduction chains are explored for the multiple orbit problem. One realization of the u sub ( sub q sub ) (2) subalgebra is associated with the valence isospin, other reductions describe coupling between identical nucleons or proton-neutron pairs. Microscopic non-deformed and deformed Hamiltonians are expressed in terms of the generators of the sp(4) and sp sub q (4) algebras. In both cases eigenvalues of the isospin breaking Hamiltonian are fit to experimental ground state energies. The theory can be used to investigate the origin of the deformation and predict binding energies of nuclei in proton-rich regions. The q-deformation parameter changes the pairing strength and in so doing introduces a non-linear coupling into the collective degree of freedom
Chiral symmetry restoration and pion properties in a q-deformed NJL model
International Nuclear Information System (INIS)
Timoteo, V.S.; Lima, C.L.
2006-01-01
We review the implementation of a q-deformed fermionic algebra in the Nambu-Jona-Lasinio model (NJL). The gap equations obtained from a deformed condensate as well as from the deformation of the NJL Hamiltonian are discussed. The effect of both temperature and deformation in the chiral symmetry restoration process as well as in the pion properties is studied. (author)
Covariant description of Hamiltonian form for field dynamics
International Nuclear Information System (INIS)
Ozaki, Hiroshi
2005-01-01
Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface
National Research Council Canada - National Science Library
Nabach, William A
2003-01-01
... in a combination of frictional and adiabatic heating due to plastic deformation. A stirring effect results in the formation of a zone of severe shear deformation and local temperatures approaching...
Tran, Henry K.; Stanton, John F.; Miller, Terry A.
2018-01-01
The limitations associated with the common practice of fitting a quadratic Hamiltonian to vibronic levels of a Jahn-Teller system have been explored quantitatively. Satisfactory results for the prototypical X∼2E‧ state of Li3 are obtained from fits to both experimental spectral data and to an "artificial" spectrum calculated by a quartic Hamiltonian which accurately reproduces the adiabatic potential obtained from state-of-the-art quantum chemistry calculations. However the values of the Jahn-Teller parameters, stabilization energy, and pseudo-rotation barrier obtained from the quadratic fit differ markedly from those associated with the ab initio potential. Nonetheless the RMS deviations of the fits are not strikingly different. Guidelines are suggested for comparing parameters obtained from fits to experiment to those obtained by direct calculation, but a principal conclusion of this work is that such comparisons must be done with a high degree of caution.
Shear Strains, Strain Rates and Temperature Changes in Adiabatic Shear Bands
1980-05-01
X14A. It has been found that when bainitic and martensitic steels are sheared adiabatically, a layer of material within ths shear zone is altezed and...Sooiety for Metals, Metals Park, Ohio, 1978, pp. 148-0. 21 TABLE II SOLID-STATE TRANSFORMATIONS IN BAINITIC STEEL TRANSFORMATION TRANSFORMATION...shear, thermoplastic, plasticity, plastic deformation, armor, steel IL AnSRACT ( -=nba asoa.tm a naeoesM iN faity by bleak n bet/2972 Experiments
Nuclear Collective Hamiltonian and Deformations; Yadernyj kollektivnyj gamil'tonian i deformatsii
Energy Technology Data Exchange (ETDEWEB)
Kumar, Krishna [Niels Bohr Institute, University of Copenhagen, Copenhagen (Denmark)
1968-12-15
The scope and limitations of a recently developed treatment of collective quadrupole motion of even-even nuclei are reviewed. This method is based on Bohr's collective Hamiltonian and the pairing-plus-quadrupole model. With an exact, numerical treatment of the couplings between the five components of quadrupole motion, the theory is able to explain and predict many trends in the low-lying levels and electromagnetic moments of nuclei in the W-Os-Pt region. The zero-point quantal motion plays an important role in spreading the nuclear wave-function in the {beta}-{gamma} plane so that the nucleus is affected essentially by the behaviour of the collective Hamiltonian away from the equilibrium shape. The {gamma} -dependence of the Hamiltonian, especially the prolate-oblate difference term of the potential function, plays a crucial role in the splitting of the 2'{sup +} and 4{sup +} states and the non-zero quadrupole moments of I {ne} 0 states, which can occur even if the equilibrium shape is spherical or completely asymmetric with {gamma} = 30 Degree-Sign . The anharmonicities of the six inertial functions of Bohr's Hamiltonian cause {beta}-{gamma} band-mixing in the W isotopes, reduce the ground-{beta}-{gamma} band-mixing in the Os isotopes, and counteract the prolate-oblate difference term so that the spectrum of the calculated {sup 196}Pt appears to be vibrational. The calculation for {sup 196}Pt gives a large, oblate quadrupole moment of the first 2{sup +} state as well as a small cross-over transition from the ground state to the second 2{sup +} state. However, the calculated 2+ states of {sup 192-196}Pt are too high by 0.1-0.2 MeV, and the calculated B(E2; 2{yields}2') values for the region are too large by about a factor of two. Some possible ways of improvement are indicated. (author) [Russian] Rassmatrivajutsja vozmozhnosti i ogranichenija nedavno razvitoj traktovki kollektivnogo kvadrupol'nogo dvizhenija v chetno-chetnyh jadrah. Jetot metod osnovan na
Energy Technology Data Exchange (ETDEWEB)
Bravetti, Alessandro, E-mail: alessandro.bravetti@iimas.unam.mx [Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Cruz, Hans, E-mail: hans@ciencias.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A. P. 70543, México, DF 04510 (Mexico); Tapias, Diego, E-mail: diego.tapias@nucleares.unam.mx [Facultad de Ciencias, Universidad Nacional Autónoma de México, A.P. 70543, México, DF 04510 (Mexico)
2017-01-15
In this work we introduce contact Hamiltonian mechanics, an extension of symplectic Hamiltonian mechanics, and show that it is a natural candidate for a geometric description of non-dissipative and dissipative systems. For this purpose we review in detail the major features of standard symplectic Hamiltonian dynamics and show that all of them can be generalized to the contact case.
The adiabatic approximation in multichannel scattering
International Nuclear Information System (INIS)
Schulte, A.M.
1978-01-01
Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)
A partial Hamiltonian approach for current value Hamiltonian systems
Naz, R.; Mahomed, F. M.; Chaudhry, Azam
2014-10-01
We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and then apply it to two widely used economic growth models: the Ramsey model with a constant relative risk aversion (CRRA) utility function and Cobb Douglas technology and a one-sector AK model of endogenous growth are considered. We show that our newly developed systematic approach can be used to deduce results given in the literature and also to find new solutions.
Deformed Fredkin spin chain with extensive entanglement
Salberger, Olof; Udagawa, Takuma; Zhang, Zhao; Katsura, Hosho; Klich, Israel; Korepin, Vladimir
2017-06-01
We introduce a new spin chain which is a deformation of the Fredkin spin chain and has a phase transition between bounded and extensive entanglement entropy scaling. In this chain, spins have a local interaction of three nearest neighbors. The Hamiltonian is frustration-free and its ground state can be described analytically as a weighted superposition of Dyck paths that depends on a deformation parameter t. In the purely spin 1/2 case, whenever t\
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
Cross-polarization phenomena in the NMR of fast spinning solids subject to adiabatic sweeps
Energy Technology Data Exchange (ETDEWEB)
Wi, Sungsool, E-mail: sungsool@magnet.fsu.edu, E-mail: lucio.frydman@weizmann.ac.il; Gan, Zhehong [National High Magnetic Field Laboratory, Tallahassee, Florida 32304 (United States); Schurko, Robert [Department of Chemistry and Biochemistry, University of Windsor, 401 Sunset Avenue, Windsor N9B 3P4, Ontario (Canada); Frydman, Lucio, E-mail: sungsool@magnet.fsu.edu, E-mail: lucio.frydman@weizmann.ac.il [National High Magnetic Field Laboratory, Tallahassee, Florida 32304 (United States); Department of Chemical Physics, Weizmann Institute of Sciences, 76100 Rehovot (Israel)
2015-02-14
Cross-polarization magic-angle spinning (CPMAS) experiments employing frequency-swept pulses are explored within the context of obtaining broadband signal enhancements for rare spin S = 1/2 nuclei at very high magnetic fields. These experiments employ adiabatic inversion pulses on the S-channel ({sup 13}C) to cover a wide frequency offset range, while simultaneously applying conventional spin-locking pulse on the I-channel ({sup 1}H). Conditions are explored where the adiabatic frequency sweep width, Δν, is changed from selectively irradiating a single magic-angle-spinning (MAS) spinning centerband or sideband, to sweeping over multiple sidebands. A number of new physical features emerge upon assessing the swept-CP method under these conditions, including multiple zero- and double-quantum CP transfers happening in unison with MAS-driven rotary resonance phenomena. These were examined using an average Hamiltonian theory specifically designed to tackle these experiments, with extensive numerical simulations, and with experiments on model compounds. Ultrawide CP profiles spanning frequency ranges of nearly 6⋅γB{sub 1}{sup s} were predicted and observed utilizing this new approach. Potential extensions and applications of this extremely broadband transfer conditions are briefly discussed.
Adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems
International Nuclear Information System (INIS)
Baranger, M.; Veneroni, M.
1978-01-01
We show how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and we start from the time-dependent Hartree-Fock equation. To this we add the adiabatic approximation, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The crucial step is the decomposition of the single-particle density matrix p in the form exp(i/sub chi/) rho/sub omicron/exp(-i/sub chi/), where rho/sub omicron/ represents a time-even Slater determinant and plays the role of coordinate. Then chi plays the role of momentum, and the adiabatic assumption is that chi is small. The energy is expanded in powers of chi, the zeroth-order being the collective potential energy. The analogy with classical mechanics is stressed and studied. The same adiabatic equations of motion are derived in three different ways (directly, from the Lagrangian, from the Hamiltonian), thus proving the consistency of the theory. The dynamical equation is not necessary for writing the energy or for the subsequent quantization which leads to a Schroedinger equation, but it must be used to check the validity of various approximation schemes, particularly to reduce the problem to a few degrees of freedom. The role of the adiabatic hypothesis, its definition, and range of validity, are analyzed in great detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given, and the moment of inertia under rotation is that of Thouless and Valatin. For a quadrupole two-body force, the Baranger-Kumar formalism is recovered. The self-consistency brings additional terms to the Inglis cranking formula. Comparison is also made with generator coordinate methods
Hamiltonian Algorithm Sound Synthesis
大矢, 健一
2013-01-01
Hamiltonian Algorithm (HA) is an algorithm for searching solutions is optimization problems. This paper introduces a sound synthesis technique using Hamiltonian Algorithm and shows a simple example. "Hamiltonian Algorithm Sound Synthesis" uses phase transition effect in HA. Because of this transition effect, totally new waveforms are produced.
Identity of the SU(3) model phenomenological hamiltonian and the hamiltonian of nonaxial rotator
International Nuclear Information System (INIS)
Filippov, G.F.; Avramenko, V.I.; Sokolov, A.M.
1984-01-01
Interpretation of nonspheric atomic nuclei spectra on the basis of phenomenological hamiltonians of SU(3) model showed satisfactory agreement of simulation calculations with experimental data. Meanwhile physical sense of phenomenological hamiltonians was not yet discussed. It is shown that phenomenological hamiltonians of SU(3) model are reduced to hamiltonian of nonaxial rotator but with additional items of the third and fourth powers angular momentum operator of rotator
Decoherence in adiabatic quantum computation
Albash, Tameem; Lidar, Daniel A.
2015-06-01
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master-equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed-system setting, remain beneficial in the open-system setting. To address the high computational cost of master-equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.
Quantum revivals, geometric phases and circle map recurrences
International Nuclear Information System (INIS)
Seshadri, S.; Lakshmibala, S.; Balakrishnan, V.
1999-01-01
Revivals of the coherent states of a deformed, adiabatically and cyclically varying oscillator Hamiltonian are examined. The revival time distribution is exactly that of Poincare recurrences for a rotation map: only three distinct revival times can occur, with specified weights. A link is thus established between quantum revivals and recurrences in a coarse-grained discrete-time dynamical system. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
An infinite family of superintegrable deformations of the Coulomb potential
International Nuclear Information System (INIS)
Post, Sarah; Winternitz, Pavel
2010-01-01
We introduce a new family of Hamiltonians with a deformed Kepler-Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wavefunctions. We show that this system is related, via coupling constant metamorphosis, to a family of superintegrable deformations of the harmonic oscillator given by Tremblay, Turbiner and Winternitz. In doing so, we prove that all Hamiltonians with an oscillator term are related by coupling constant metamorphosis to systems with a Kepler-Coulomb term, both on Euclidean space. We also look at the effect of the transformation on the integrals of the motion, the classical trajectories and the wavefunctions, and give the transformed integrals explicitly for the classical system. (fast track communication)
An infinite family of superintegrable deformations of the Coulomb potential
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah [Centre de recherches mathematiques, CP 6128 succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada); Winternitz, Pavel, E-mail: post@CRM.UMontreal.C, E-mail: wintern@CRM.UMontreal.C [Centre de recherches mathematiques and Departement de mathematiques et de statistique, CP 6128 succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada)
2010-06-04
We introduce a new family of Hamiltonians with a deformed Kepler-Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wavefunctions. We show that this system is related, via coupling constant metamorphosis, to a family of superintegrable deformations of the harmonic oscillator given by Tremblay, Turbiner and Winternitz. In doing so, we prove that all Hamiltonians with an oscillator term are related by coupling constant metamorphosis to systems with a Kepler-Coulomb term, both on Euclidean space. We also look at the effect of the transformation on the integrals of the motion, the classical trajectories and the wavefunctions, and give the transformed integrals explicitly for the classical system. (fast track communication)
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1994-01-01
Fluid mechanics is examined from a Hamiltonian perspective. The Hamiltonian point of view provides a unifying framework; by understanding the Hamiltonian perspective, one knows in advance (within bounds) what answers to expect and what kinds of procedures can be performed. The material is organized into five lectures, on the following topics: rudiments of few-degree-of-freedom Hamiltonian systems illustrated by passive advection in two-dimensional fluids; functional differentiation, two action principles of mechanics, and the action principle and canonical Hamiltonian description of the ideal fluid; noncanonical Hamiltonian dynamics with examples; tutorial on Lie groups and algebras, reduction-realization, and Clebsch variables; and stability and Hamiltonian systems
Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas
International Nuclear Information System (INIS)
Becoulet, A.; Gambier, D.J.; Samain, A.
1990-03-01
The question of heating a tokamak plasma by means of electromagnetic waves in the Ion Cyclotron Range of Frequency (ICRF) is considered in the perspective of large RF powers and in the low collisionality regime. In such case the Quasi Linear Theory (QLT) is validated by the Hamiltonian dynamics of the wave particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows to derive the RF diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. Then the Fokker Planck equation is given a variational from which a solution is derived in the form of a semi analytical trial function of three parameters: the percentage of resonant particle contained in the tail; an isotropic width ΔT and an anisotropic one ΔP. This solution is successfully tested against real experimental observations. Practically it is shown that in the case of JET the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that of a bounce averaged prediction. This may actually be an advantage for machines like JET considering the energy range required to simulate the α-particle behaviour in a relevant fusion reactor
Adiabatic shear localization in a near beta Ti–5Al–5Mo–5 V–1Cr–1Fe alloy
Energy Technology Data Exchange (ETDEWEB)
Wang, Bingfeng, E-mail: biw009@ucsd.edu [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); Key Lab of Nonferrous Materials, Ministry of Education, Central South University, Changsha 410083, Hunan (China); Department of Mechanical and Aerospace Engineering, University of California, San Diego (United States); Sun, Jieying; Wang, Xiaoyan; Fu, Ao [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China)
2015-07-15
Adiabatic shear localization plays an important role in the deformation and failure of near beta Ti–5Al–5Mo–5 V–1Cr–1Fe alloy used in aircraft's gear at high rate deformation. Hat shaped specimens with different nominal shear strains are used to induce the formation of an adiabatic shear band under controlled shock-loading experiments. When the nominal shear strain is about 0.68, unstable shear deformation of the alloy emerges after the true flow stress reaches 1100 MPa, the first vibration peak during the split Hopkinson pressure bar testing, and the whole process lasts about 62 μs. The microstructures within the shear band in the Ti–5Al–5Mo–5V–1Cr–1Fe alloy are investigated by means of optical microscopy, scanning electron microscopy and transmission electron microscopy. Phase transformation occurs in the shear band when the nominal shear strain increases to 0.68. A number of equiaxed grains with sizes 50–200 nm and alpha″-phase are in the center of the shear band. Kinetic calculations indicate that during the deformation process, the recrystallized nanosized grains can be formed in the shear band by way of the subgrain boundaries rotation, and the alpha″ phase transformation start after the subgrain boundaries rotated to 30°.
International Nuclear Information System (INIS)
Bakalov, D.D.; Melezhik, V.S.
1987-01-01
The relativistic Hamiltonian for 3-spin particles with electromagnetic interaction has been represented in the form of a sum of terms with factorized dependence on spin, angular and spheroidal variable, and its matrix elements have been expressed in terms of the matrix elements of a small number of ''basic'' operators. The numerical values of the latter have been tabulated, thus allowing for the evaluation of the leading relativistic effects in any 3-body system (with unit particle charge) with and accuracy of ∼ 0(1/2M), where 1/2M=(M 1 -1 +M 2 -1 )/2(M 1 -1 +M 3 -1 ) is the small parameter of the adiabatic expansion (M i , i=1,2,3 being particle masses)
Proton-neutron sdg boson model and spherical-deformed phase transition
Otsuka, Takaharu; Sugita, Michiaki
1988-12-01
The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.
Proton-neutron sdg boson model and spherical-deformed phase transition
Energy Technology Data Exchange (ETDEWEB)
Otsuka, Takaharu; Sugita, Michiaki
1988-12-15
The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing + quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.
Adiabatic capture and debunching
International Nuclear Information System (INIS)
Ng, K.Y.
2012-01-01
In the study of beam preparation for the g-2 experiment, adiabatic debunching and adiabatic capture are revisited. The voltage programs for these adiabbatic processes are derived and their properties discussed. Comparison is made with some other form of adiabatic capture program. The muon g-2 experiment at Fermilab calls for intense proton bunches for the creation of muons. A booster batch of 84 bunches is injected into the Recycler Ring, where it is debunched and captured into 4 intense bunches with the 2.5-MHz rf. The experiment requires short bunches with total width less than 100 ns. The transport line from the Recycler to the muon-production target has a low momentum aperture of ∼ ±22 MeV. Thus each of the 4 intense proton bunches required to have an emittance less than ∼ 3.46 eVs. The incoming booster bunches have total emittance ∼ 8.4 eVs, or each one with an emittance ∼ 0.1 eVs. However, there is always emittance increase when the 84 booster bunches are debunched. There will be even larger emittance increase during adiabatic capture into the buckets of the 2.5-MHz rf. In addition, the incoming booster bunches may have emittances larger than 0.1 eVs. In this article, we will concentrate on the analysis of the adiabatic capture process with the intention of preserving the beam emittance as much as possible. At this moment, beam preparation experiment is being performed at the Main Injector. Since the Main Injector and the Recycler Ring have roughly the same lattice properties, we are referring to adiabatic capture in the Main Injector instead in our discussions.
Q-deformed systems and constrained dynamics
International Nuclear Information System (INIS)
Shabanov, S.V.
1993-01-01
It is shown that quantum theories of the q-deformed harmonic oscillator and one-dimensional free q-particle (a free particle on the 'quantum' line) can be obtained by the canonical quantization of classical Hamiltonian systems with commutative phase-space variables and a non-trivial symplectic structure. In the framework of this approach, classical dynamics of a particle on the q-line coincides with the one of a free particle with friction. It is argued that q-deformed systems can be treated as ordinary mechanical systems with the second-class constraints. In particular, second-class constrained systems corresponding to the q-oscillator and q-particle are given. A possibility of formulating q-deformed systems via gauge theories (first-class constrained systems) is briefly discussed. (orig.)
Anyons, deformed oscillator algebras and projectors
International Nuclear Information System (INIS)
Engquist, Johan
2009-01-01
We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter ν. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.
Wireless adiabatic power transfer
International Nuclear Information System (INIS)
Rangelov, A.A.; Suchowski, H.; Silberberg, Y.; Vitanov, N.V.
2011-01-01
Research highlights: → Efficient and robust mid-range wireless energy transfer between two coils. → The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. → Wireless energy transfer is insensitive to any resonant constraints. → Wireless energy transfer is insensitive to noise in the neighborhood of the coils. - Abstract: We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
Proton-neutron sdg boson model and spherical-deformed phase transition
International Nuclear Information System (INIS)
Otsuka, Takaharu; Sugita, Michiaki
1988-01-01
The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing + quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects. (orig.)
Lobe, Elisabeth; Stollenwerk, Tobias; Tröltzsch, Anke
2015-01-01
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic ...
Hamiltonian analysis of a magnetoelectroelastic notch in a mode III singularity
International Nuclear Information System (INIS)
Zhou, Z H; Xu, X S; Leung, A Y T
2013-01-01
The stress intensity factor (SIF) of a multi-material magnetoelectroelastic wedge in anti-plane deformation is analytically determined by the symplectic method. The Lagrangian equations in configuration variables alone are transformed to Hamiltonian equations in dual variables (configuration and momentum) which allow the use of the method of separation of variables. The solutions of the Hamiltonian equations can be expanded analytically in terms of the symplectic eigenfunctions with coefficients to be determined by the boundary conditions. For the wedge problem, the pairs of anti-plane displacements and shear stresses, electric fields and electric displacements, and magnetic fields and magnetic inductions are proved to be the dual (momentum) variables of the configuration variables. The singularity orders depend directly on the first few eigenvalues whose real parts are less than one but greater than zero. Numerical results for various conditions show the variations of the singularity orders. In particular, special behaviors of the order of the singularity for some special wedge angles are noted. (paper)
Universal fault-tolerant adiabatic quantum computing with quantum dots or donors
Landahl, Andrew
I will present a conceptual design for an adiabatic quantum computer that can achieve arbitrarily accurate universal fault-tolerant quantum computations with a constant energy gap and nearest-neighbor interactions. This machine can run any quantum algorithm known today or discovered in the future, in principle. The key theoretical idea is adiabatic deformation of degenerate ground spaces formed by topological quantum error-correcting codes. An open problem with the design is making the four-body interactions and measurements it uses more technologically accessible. I will present some partial solutions, including one in which interactions between quantum dots or donors in a two-dimensional array can emulate the desired interactions in second-order perturbation theory. I will conclude with some open problems, including the challenge of reformulating Kitaev's gadget perturbation theory technique so that it preserves fault tolerance. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
General technique to produce isochronous Hamiltonians
International Nuclear Information System (INIS)
Calogero, F; Leyvraz, F
2007-01-01
We introduce a new technique-characterized by an arbitrary positive constant Ω, with which we associate the period T = 2π/Ω-to 'Ω-modify' a Hamiltonian so that the new Hamiltonian thereby obtained is entirely isochronous, namely it yields motions all of which (except possibly for a lower dimensional set of singular motions) are periodic with the same fixed period T in all their degrees of freedom. This technique transforms real autonomous Hamiltonians into Ω-modified Hamiltonians which are also real and autonomous, and it is widely applicable, for instance, to the most general many-body problem characterized by Newtonian equations of motion ('acceleration equal force') provided it is translation invariant. The Ω-modified Hamiltonians are of course not translation invariant, but for Ω = 0 they reduce (up to marginal changes) to the unmodified Hamiltonians they were obtained from. Hence, when this technique is applied to translation-invariant Hamiltonians yielding, in their center-of-mass systems, chaotic motions with a natural time scale much smaller than T, the corresponding Ω-modified Hamiltonians shall display a chaotic behavior for quite some time before the isochronous character of the motions takes over. We moreover show that the quantized versions of these Ω-modified Hamiltonians feature equispaced spectra
Ion Motion in the Adiabatic Focuser
International Nuclear Information System (INIS)
Henestroza, E.; Sessler, A.M.; Yu, S.S.
2006-01-01
In this paper we numerically study the effect of ion motion in an adiabatic focuser, motivated by a recent suggestion that ion motion in an adiabatic focuser might be significant and even preclude operation of the focuser as previously envisioned. It is shown that despite ion motion the adiabatic focuser should work as well as originally envisioned
International Nuclear Information System (INIS)
Hoover, W.G.; Evans, D.J.; Hickman, R.B.; Ladd, A.J.C.; Ashurst, W.T.; Moran, B.
1980-01-01
A new Hamiltonian method for deformation simulations is related to the Green-Kubo fluctuation theory through perturbation theory and linear-response theory. Numerical results for the bulk and shear viscosity coefficients are compared to corresponding Green-Kubo calculations. Both viscosity coefficients depend similarly on frequency, in a way consistent with enhanced ''long-time tails.''
q-Power function over q-commuting variables and deformed XXX, XXZ chains
International Nuclear Information System (INIS)
Khoroshkin, S.M.; Stolin, A.A.; Tolstoy, V.N.
2001-01-01
Certain functional identifies for the Gauss q-power function of a sum of q-commuting variables are found. Then these identifies are used to obtain two-parameter twists of the quantum affine algebra U q (sl 2 ) and of the Yangian Y(sl 2 ). The corresponding deformed trigonometric and rational quantum R matrices, which then are used in the computation of deformed XXX and XXZ Hamiltonians [ru
Adiabatic temperature change from non-adiabatic measurements
Czech Academy of Sciences Publication Activity Database
Carvalho, A.M.G.; Mejía, C.S.; Ponte, C.A.; Silva, L.E.L.; Kaštil, Jiří; Kamarád, Jiří; Gomes, A.M.
2016-01-01
Roč. 122, č. 3 (2016), s. 1-5, č. článku 246. ISSN 0947-8396 Institutional support: RVO:68378271 Keywords : magnetocaloric effect * adiabatic temperature change * calorimetric device * gadolinium Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.455, year: 2016
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Rabli, Djamal; McCarroll, Ronald
2018-02-01
This review surveys the different theoretical approaches, used to describe inelastic and rearrangement processes in collisions involving atoms and ions. For a range of energies from a few meV up to about 1 keV, the adiabatic representation is expected to be valid and under these conditions, inelastic and rearrangement processes take place via a network of avoided crossings of the potential energy curves of the collision system. In general, such avoided crossings are finite in number. The non-adiabatic coupling, due to the breakdown of the Born-Oppenheimer separation of the electronic and nuclear variables, depends on the ratio of the electron mass to the nuclear mass terms in the total Hamiltonian. By limiting terms in the total Hamiltonian correct to first order in the electron to nuclear mass ratio, a system of reaction coordinates is found which allows for a correct description of both inelastic channels. The connection between the use of reaction coordinates in the quantum description and the electron translation factors of the impact parameter approach is established. A major result is that only when reaction coordinates are used, is it possible to introduce the notion of a minimal basis set. Such a set must include all avoided crossings including both radial coupling and long range Coriolis coupling. But, only when reactive coordinates are used, can such a basis set be considered as complete. In particular when the centre of nuclear mass is used as centre of coordinates, rather than the correct reaction coordinates, it is shown that erroneous results are obtained. A few results to illustrate this important point are presented: one concerning a simple two-state Landau-Zener type avoided crossing, the other concerning a network of multiple crossings in a typical electron capture process involving a highly charged ion with a neutral atom.
Multi-quasiparticle high-K isomeric states in deformed nuclei
Directory of Open Access Journals (Sweden)
Xu F. R.
2016-01-01
Full Text Available In the past years, we have made many theoretical investigations on multi-quasiparticle high-K isomeric states. A deformation-pairing-configuration self-consistent calculation has been developed by calculating a configuration-constrained multi-quasiparticle potential energy surface (PES. The specific single-particle orbits that define the high-K configuration are identified and tracked (adiabatically blocked by calculating the average Nilsson numbers. The deformed Woods-Saxon potential was taken to give single-particle orbits. The configuration-constrained PES takes into account the shape polarization effect. Such calculations give good results on excitation energies, deformations and other structure information about multi-quasiparticle high-K isomeric states. Many different mass regions have been investigated.
DEFF Research Database (Denmark)
Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir
2007-01-01
The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1984-03-01
The magnetic field line Hamiltonian and the associated canonical form for the magnetic field are important concepts both for understanding toroidal plasma physics and for practical calculations. A number of important properties of the canonical or Hamiltonian representation are derived and their importance is explained
Canonical transformations and hamiltonian path integrals
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Behaviour of the Hamiltonian path integrals under canonical transformations produced by a generator, is investigated. An exact form is determined for the kernel of the unitary operator realizing the corresponding quantum transformation. Equivalence rules are found (the Hamiltonian formalism, one-dimensional case) enabling one to exclude non-standard terms from the action. It is shown that the Hamiltonian path integral changes its form under cononical transformations: in the transformed expression besides the classical Hamiltonian function there appear some non-classical terms
Piecewise adiabatic following in non-Hermitian cycling
Gong, Jiangbin; Wang, Qing-hai
2018-05-01
The time evolution of periodically driven non-Hermitian systems is in general nonunitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for nonunitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of nonunitary dynamics in cases of slow cycling and should stimulate future applications of nonunitary dynamics.
Perspective: Quantum Hamiltonians for optical interactions
Andrews, David L.; Jones, Garth A.; Salam, A.; Woolley, R. Guy
2018-01-01
The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.
International Nuclear Information System (INIS)
Grady, D.E.; Asav, J.R.; Rohde, R.W.; Wise, J.L.
1983-01-01
This chapter attempts to correlate the shock compression and quasistatic deformation of 6061-T6 aluminium. Examines recovered specimens which have been shock loaded, and compares results with both static and dynamic mechanical property measurements. Discusses experimental procedures (reshock and unloading experiments, shock recovery techniques, metallographic techniques and coldwork experiments); dynamic strength and wave-profile properties (strength and shear-stress states on the Hugoniot, steady-wave risetime and viscosity); quasistatic and shock metallography studies (metallography of quasistatically deformed material; metallography of shock deformed specimens; comparison of static and shock deformation; correlation of hardness and dynamic strength measurements); and thermal trapping calculations in shocked aluminium (heterogeneous deformation and adiabatic heating in shock-wave loading; energy and risetime relations under steadywave shock compression; heterogeneous temperature calculations in aluminium). Concludes that heterogeneous shear deformation appears to play a role in the dynamic deformation process
Notch filters for port-Hamiltonian systems
Dirksz, D.A.; Scherpen, J.M.A.; van der Schaft, A.J.; Steinbuch, M.
2012-01-01
In this paper a standard notch filter is modeled in the port-Hamiltonian framework. By having such a port-Hamiltonian description it is proven that the notch filter is a passive system. The notch filter can then be interconnected with another (nonlinear) port-Hamiltonian system, while preserving the
International Nuclear Information System (INIS)
Rogers, C; Schief, W K
2011-01-01
A 2+1-dimensional version of a non-isothermal gas dynamic system with origins in the work of Ovsiannikov and Dyson on spinning gas clouds is shown to admit a Hamiltonian reduction which is completely integrable when the adiabatic index γ = 2. This nonlinear dynamical subsystem is obtained via an elliptic vortex ansatz which is intimately related to the construction of a Lax pair in the integrable case. The general solution of the gas dynamic system is derived in terms of Weierstrass (elliptic) functions. The latter derivation makes use of a connection with a stationary nonlinear Schrödinger equation and a Steen–Ermakov–Pinney equation, the superposition principle of which is based on the classical Lamé equation
Non-adiabatic perturbations in multi-component perfect fluids
Energy Technology Data Exchange (ETDEWEB)
Koshelev, N.A., E-mail: koshna71@inbox.ru [Ulyanovsk State University, Leo Tolstoy str 42, 432970 (Russian Federation)
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Non-adiabatic perturbations in multi-component perfect fluids
International Nuclear Information System (INIS)
Koshelev, N.A.
2011-01-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models
Collective Hamiltonians for dipole giant resonances
International Nuclear Information System (INIS)
Weiss, L.I.
1991-07-01
The collective hamiltonian for the Giant Dipole resonance (GDR), in the Goldhaber-Teller-Model, is analytically constructed using the semiclassical and generator coordinates method. Initially a conveniently parametrized set of many body wave functions and a microscopic hamiltonian, the Skyrme hamiltonian - are used. These collective Hamiltonians are applied to the investigation of the GDR, in He 4 , O 16 and Ca 40 nuclei. Also the energies and spectra of the GDR are obtained in these nuclei. The two sets of results are compared, and the zero point energy effects analysed. (author)
On the domain of the Nelson Hamiltonian
Griesemer, M.; Wünsch, A.
2018-04-01
The Nelson Hamiltonian is unitarily equivalent to a Hamiltonian defined through a closed, semibounded quadratic form, the unitary transformation being explicitly known and due to Gross. In this paper, we study the mapping properties of the Gross-transform in order to characterize the regularity properties of vectors in the form domain of the Nelson Hamiltonian. Since the operator domain is a subset of the form domain, our results apply to vectors in the domain of the Hamiltonian as well. This work is a continuation of our previous work on the Fröhlich Hamiltonian.
Geometric Hamiltonian structures and perturbation theory
International Nuclear Information System (INIS)
Omohundro, S.
1984-08-01
We have been engaged in a program of investigating the Hamiltonian structure of the various perturbation theories used in practice. We describe the geometry of a Hamiltonian structure for non-singular perturbation theory applied to Hamiltonian systems on symplectic manifolds and the connection with singular perturbation techniques based on the method of averaging
Relation of deformed nonlinear algebras with linear ones
International Nuclear Information System (INIS)
Nowicki, A; Tkachuk, V M
2014-01-01
The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Quantum adiabatic Markovian master equations
International Nuclear Information System (INIS)
Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A
2012-01-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)
Time dependent drift Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1982-04-01
The motion of individual charged particles in a given magnetic and an electric fields is discussed. An idea of a guiding center distribution function f is introduced. The guiding center distribution function is connected to the asymptotic Hamiltonian through the drift kinetic equation. The general non-stochastic magnetic field can be written in a contravariant and a covariant forms. The drift Hamiltonian is proposed, and the canonical gyroradius is presented. The proposed drift Hamiltonian agrees with Alfven's drift velocity to lowest non-vanishing order in the gyroradius. The relation between the exact, time dependent equations of motion and the guiding center equation is clarified by a Lagrangian analysis. The deduced Lagrangian represents the drift motion. (Kato, T.)
On the moment of inertia of a quantum harmonic oscillator
International Nuclear Information System (INIS)
Khamzin, A. A.; Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.
2013-01-01
An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.
Magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Boozer, A.H.
1985-02-01
The basic properties of the Hamiltonian representation of magnetic fields in canonical form are reviewed. The theory of canonical magnetic perturbation theory is then developed and applied to the time evolution of a magnetic field embedded in a toroidal plasma. Finally, the extension of the energy principle to tearing modes, utilizing the magnetic field line Hamiltonian, is outlined
Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics
International Nuclear Information System (INIS)
Sarovar, Mohan; Young, Kevin C
2013-01-01
While adiabatic quantum computing (AQC) has some robustness to noise and decoherence, it is widely believed that encoding, error suppression and error correction will be required to scale AQC to large problem sizes. Previous works have established at least two different techniques for error suppression in AQC. In this paper we derive a model for describing the dynamics of encoded AQC and show that previous constructions for error suppression can be unified with this dynamical model. In addition, the model clarifies the mechanisms of error suppression and allows the identification of its weaknesses. In the second half of the paper, we utilize our description of non-equilibrium dynamics in encoded AQC to construct methods for error correction in AQC by cooling local degrees of freedom (qubits). While this is shown to be possible in principle, we also identify the key challenge to this approach: the requirement of high-weight Hamiltonians. Finally, we use our dynamical model to perform a simplified thermal stability analysis of concatenated-stabilizer-code encoded many-body systems for AQC or quantum memories. This work is a companion paper to ‘Error suppression and error correction in adiabatic quantum computation: techniques and challenges (2013 Phys. Rev. X 3 041013)’, which provides a quantum information perspective on the techniques and limitations of error suppression and correction in AQC. In this paper we couch the same results within a dynamical framework, which allows for a detailed analysis of the non-equilibrium dynamics of error suppression and correction in encoded AQC. (paper)
Single-particle dynamics - Hamiltonian formulation
International Nuclear Information System (INIS)
Montague, B.W.
1977-01-01
In this paper the Hamiltonian formalism is applied to the linear theory of accelerator dynamics. The reasons for the introduction of this method rather than the more straightforward use of second order differential equations of motion are briefly discussed. An outline of Lagrangian and Hamiltonian formalism is given, some properties of the Hamiltonian are discussed and canonical transformations are illustrated. The methods are demonstrated using elementary examples such as the simple pendulum and the procedures adopted to handle specific problems in accelerator theory are indicated. (B.D.)
Effective field theory for triaxially deformed nuclei
Energy Technology Data Exchange (ETDEWEB)
Chen, Q.B. [Technische Universitaet Muechen, Physik-Department, Garching (Germany); Peking University, State Key Laboratory of Nuclear Physics and Technology, School of Physics, Beijing (China); Kaiser, N. [Technische Universitaet Muechen, Physik-Department, Garching (Germany); Meissner, Ulf G. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Institute for Advanced Simulation, Institut fuer Kernphysik, Juelich Center for Hadron Physics and JARA-HPC, Forschungszentrum Juelich, Juelich (Germany); Meng, J. [Peking University, State Key Laboratory of Nuclear Physics and Technology, School of Physics, Beijing (China); Beihang University, School of Physics and Nuclear Energy Engineering, Beijing (China); University of Stellenbosch, Department of Physics, Stellenbosch (South Africa)
2017-10-15
Effective field theory is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. The Hamiltonian for the triaxial rotor is obtained up to next-to-leading order within the effective field theory formalism. Its applicability is examined by comparing with a five-dimensional rotor-vibrator Hamiltonian for the description of the energy spectra of the ground state and γ band in Ru isotopes. It is found that by taking into account the next-to-leading order corrections, the ground state band in the whole spin region and the γ band in the low spin region are well described. The deviations for high-spin states in the γ bands point towards the importance of including vibrational degrees of freedom in the effective field theory formulation. (orig.)
The Hamiltonian of QED. Zero mode
International Nuclear Information System (INIS)
Zastavenko, L.G.
1990-01-01
We start with the standard QED Lagrangian. New derivation of the spinor QED Hamiltonian is given. We have taken into account the zero mode. Our derivation is faultless from the point of view of gauge invariance. It gives important corrections to the standard QED Hamiltonian. Our derivation of the Hamiltonian can be generalized to the case of QCD. 5 refs
Non-adiabatic perturbations in Ricci dark energy model
International Nuclear Information System (INIS)
Karwan, Khamphee; Thitapura, Thiti
2012-01-01
We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included
Dissipative systems and Bateman's Hamiltonian
International Nuclear Information System (INIS)
Pedrosa, I.A.; Baseia, B.
1983-01-01
It is shown, by using canonical transformations, that one can construct Bateman's Hamiltonian from a Hamiltonian for a conservative system and obtain a clear physical interpretation which explains the ambiguities emerging from its application to describe dissipative systems. (Author) [pt
Symmetry of the Adiabatic Condition in the Piston Problem
Anacleto, Joaquim; Ferreira, J. M.
2011-01-01
This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be…
Diagonalization of Hamiltonian; Diagonalization of Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Garrido, L M; Pascual, P
1960-07-01
We present a general method to diagonalized the Hamiltonian of particles of arbitrary spin. In particular we study the cases of spin 0,1/2, 1 and see that for spin 1/2 our transformation agrees with Foldy's and obtain the expression for different observables for particles of spin C and 1 in the new representation. (Author) 7 refs.
Energy consumption for shortcuts to adiabaticity
Torrontegui, E.; Lizuain, I.; González-Resines, S.; Tobalina, A.; Ruschhaupt, A.; Kosloff, R.; Muga, J. G.
2017-08-01
Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.
Assessment of total efficiency in adiabatic engines
Mitianiec, W.
2016-09-01
The paper presents influence of ceramic coating in all surfaces of the combustion chamber of SI four-stroke engine on working parameters mainly on heat balance and total efficiency. Three cases of engine were considered: standard without ceramic coating, fully adiabatic combustion chamber and engine with different thickness of ceramic coating. Consideration of adiabatic or semi-adiabatic engine was connected with mathematical modelling of heat transfer from the cylinder gas to the cooling medium. This model takes into account changeable convection coefficient based on the experimental formulas of Woschni, heat conductivity of multi-layer walls and also small effect of radiation in SI engines. The simulation model was elaborated with full heat transfer to the cooling medium and unsteady gas flow in the engine intake and exhaust systems. The computer program taking into account 0D model of engine processes in the cylinder and 1D model of gas flow was elaborated for determination of many basic engine thermodynamic parameters for Suzuki DR-Z400S 400 cc SI engine. The paper presents calculation results of influence of the ceramic coating thickness on indicated pressure, specific fuel consumption, cooling and exhaust heat losses. Next it were presented comparisons of effective power, heat losses in the cooling and exhaust systems, total efficiency in function of engine rotational speed and also comparison of temperature inside the cylinder for standard, semi-adiabatic and full adiabatic engine. On the basis of the achieved results it was found higher total efficiency of adiabatic engines at 2500 rpm from 27% for standard engine to 37% for full adiabatic engine.
Quantum Hamiltonian reduction in superspace formalism
International Nuclear Information System (INIS)
Madsen, J.O.; Ragoucy, E.
1994-02-01
Recently the quantum Hamiltonian reduction was done in the case of general sl(2) embeddings into Lie algebras and superalgebras. The results are extended to the quantum Hamiltonian reduction of N=1 affine Lie superalgebras in the superspace formalism. It is shown that if we choose a gauge for the supersymmetry, and consider only certain equivalence classes of fields, then our quantum Hamiltonian reduction reduces to quantum Hamiltonian reduction of non-supersymmetric Lie superalgebras. The super energy-momentum tensor is constructed explicitly as well as all generators of spin 1 (and 1/2); thus all generators in the superconformal, quasi-superconformal and Z 2 *Z 2 superconformal algebras are constructed. (authors). 21 refs
Discrete Hamiltonian evolution and quantum gravity
International Nuclear Information System (INIS)
Husain, Viqar; Winkler, Oliver
2004-01-01
We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization
Tkatchenko, Alexandre; Ambrosetti, Alberto; DiStasio, Robert A.
2013-02-01
Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.
Accuracy versus run time in an adiabatic quantum search
International Nuclear Information System (INIS)
Rezakhani, A. T.; Pimachev, A. K.; Lidar, D. A.
2010-01-01
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.
The Motion Of A Deformable Body In - Bounded Fluid
International Nuclear Information System (INIS)
Galpert, A.R.; Miloh, T.
1998-01-01
The Hamiltonian formalism for the motion of a deformable body in an inviscid irrotational fluid is generalized for the case of the motion in a bounded fluid. We found that the presence of the boundaries in a liquid leads to the chaotization of the body's motion. The ('memory' effect connected with a free surface boundary condition is also accounted for
Generalized oscillator representations for Calogero Hamiltonians
International Nuclear Information System (INIS)
Tyutin, I V; Voronov, B L
2013-01-01
This paper is a natural continuation of the previous paper (Gitman et al 2011 J. Phys. A: Math. Theor. 44 425204), where oscillator representations for nonnegative Calogero Hamiltonians with coupling constant α ⩾ − 1/4 were constructed. In this paper, we present generalized oscillator representations for all Calogero Hamiltonians with α ⩾ − 1/4. These representations are generally highly nonunique, but there exists an optimum representation for each Hamiltonian. (comment)
Non-singular black holes and the limiting curvature mechanism: a Hamiltonian perspective
Ben Achour, J.; Lamy, F.; Liu, H.; Noui, K.
2018-05-01
We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum gravity. As expected, contrary to what happens in the cosmological sector, mimetic gravity with a limiting curvature fails to reproduce the usual effective dynamics of spherically symmetric loop quantum gravity which are generically not covariant. Nonetheless, we exhibit a theory in the class of extended mimetic gravity whose dynamics reproduces the general shape of the effective corrections of spherically symmetric polymer models, but in an undeformed covariant manner. These covariant effective corrections are found to be always metric dependent, i.e. within the bar mu-scheme, underlying the importance of this ingredient for inhomogeneous polymer models. In that respect, extended mimetic gravity can be viewed as an effective covariant theory which naturally implements a covariant notion of point wise holonomy-like corrections. The difference between the mimetic and polymer Hamiltonian formulations provides us with a guide to understand the deformation of covariance in inhomogeneous polymer models.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Spatial non-adiabatic passage using geometric phases
Energy Technology Data Exchange (ETDEWEB)
Benseny, Albert; Busch, Thomas [Okinawa Institute of Science and Technology Graduate University, Quantum Systems Unit, Okinawa (Japan); Kiely, Anthony; Ruschhaupt, Andreas [University College Cork, Department of Physics, Cork (Ireland); Zhang, Yongping [Okinawa Institute of Science and Technology Graduate University, Quantum Systems Unit, Okinawa (Japan); Shanghai University, Department of Physics, Shanghai (China)
2017-12-15
Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield the same fidelity as their adiabatic counterparts, but on fast timescales. In particular, we consider a charged particle in a system of three tunnel-coupled quantum wells, where the presence of a magnetic field can induce a geometric phase during the tunnelling processes. We show that this leads to the appearance of complex tunnelling amplitudes and allows for the implementation of spatial non-adiabatic passage. We demonstrate the ability of such a system to transport a particle between two different wells and to generate a delocalised superposition between the three traps with high fidelity in short times. (orig.)
Fast-forward of quantum adiabatic dynamics in electro-magnetic field
Masuda, Shumpei; Nakamura, Katsuhiro
2010-01-01
We show a method to accelerate quantum adiabatic dynamics of wavefunctions under electro-magnetic field by developing the previous theory (Masuda & Nakamura 2008 and 2010). Firstly we investigate the orbital dynamics of a charged particle. We derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states except for the spatially uniform phase such as the adiabatic phase in any desired short time. Fast-forward of adiabatic squeezing and tran...
On the physical applications of hyper-Hamiltonian dynamics
International Nuclear Information System (INIS)
Gaeta, Giuseppe; Rodriguez, Miguel A
2008-01-01
An extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds ('hyper-Hamiltonian dynamics') and sharing many of the attractive features of standard Hamiltonian dynamics, was introduced in previous work. In this paper, we discuss applications of the theory to physically interesting cases, dealing with the dynamics of particles with spin 1/2 in a magnetic field, i.e. the Pauli and the Dirac equations. While the free Pauli equation corresponds to a hyper-Hamiltonian flow, it turns out that the hyper-Hamiltonian description of the Dirac equation, and of the full Pauli one, is in terms of two commuting hyper-Hamiltonian flows. In this framework one can use a factorization principle discussed here (which is a special case of a general phenomenon studied by Walcher) and provide an explicit description of the resulting flow. On the other hand, by applying the familiar Foldy-Wouthuysen and Cini-Tousheck transformations (and the one recently introduced by Mulligan) which separate-in suitable limits-the Dirac equation into two equations, each of these turn out to be described by a single hyper-Hamiltonian flow. Thus the hyper-Hamiltonian construction is able to describe the fundamental dynamics for particles with spin
Oscillator representations for self-adjoint Calogero Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V; Voronov, B L, E-mail: gitman@dfn.if.usp.br, E-mail: tyutin@lpi.ru, E-mail: voronov@lpi.ru [Lebedev Physical Institute, Moscow (Russian Federation)
2011-10-21
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = {alpha}x{sup -2}. We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d{sub x}{sup 2}+{alpha}x{sup -2} for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat{sup +} a-hat and A-hat = a-hat a-hat{sup +} are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat{sup +}. An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Oscillator representations for self-adjoint Calogero Hamiltonians
International Nuclear Information System (INIS)
Gitman, D M; Tyutin, I V; Voronov, B L
2011-01-01
In Gitman et al (2010 J. Phys. A: Math. Theor. 43 145205), we presented a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential V(x) = αx -2 . We described all possible self-adjoint (s.a.) operators (s.a. Hamiltonians) associated with the differential operation H=-d x 2 +αx -2 for the Calogero Hamiltonian. Here, we discuss a new aspect of the problem, the so-called oscillator representations for the Calogero Hamiltonians. As is known, operators of the form N-hat = a-hat + a-hat and A-hat = a-hat a-hat + are called operators of oscillator type. Oscillator-type operators possess a number of useful properties in the case when the elementary operators a-hat are closed. It turns out that some s.a. Calogero Hamiltonians allow oscillator-type representations. We describe such Hamiltonians and find the corresponding mutually adjoint elementary operators a-hat and a-hat + . An oscillator-type representation for a given Hamiltonian is generally not unique. (paper)
Energy Technology Data Exchange (ETDEWEB)
Alceanu-G, Pinho de; Picard, J [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
The odd-odd deformed nuclei are described as a rotator plus two odd nucleons moving in orbitals {omega}{sub p} and {omega}{sub n} of the deformed potential. We investigate the energies and wave functions of the various states of the ({omega}{sub p}, {omega}{sub n}) configurations by calculating and numerically diagonalizing the Hamiltonian matrix (with R.P.C. and residual interactions). The Gallagher-Mosskowski coupling rules ana the abnormal K equals 0 rotational bands are discussed. (authors) [French] Les noyaux impair-impairs deformes sont decrits comme un rotateur plus deux nucleons non apparies dans les orbites {omega}{sub p} et {omega}{sub n} du potentiel deforme. Nous etudions le spectre d'energie et les fonctions d'onde des configurations ({omega}{sub p}, {omega}{sub n}) en tenant compte de l'interaction particule-rotation et de la force residuelle entre les deux nucleons celibataires.
Quantum theory of NMR adiabatic pulses and their applications
International Nuclear Information System (INIS)
Ke, Y.
1993-01-01
Recently explosive developments of in vivo NMR spectroscopy (NMRS) and imaging (NMRI) in biological and medical sciences have resulted in the establishment of NMR as one of the most advanced major technique in life sciences. These developments have created huge demands for a variety of NMR adiabatic pulses with play a very important role in NMR experiments in vivo. In order to develop new NMR adiabatic pulses, a rigorous systematical quantum theory for this kind of pulses is greatly needed. Providing such a theory is one of the important goals of this dissertation. Quantum density matrix theory and product operator method have been used throughout this dissertation. Another goal, which is the major goal of this thesis research, is to use the quantum theory as a guide to develop new NMR adiabatic pulses and their applications. To fill this goal, a technique to construct a new type of adiabatic pulses, narrow band selective adiabatic pulses, has been invented, which is described through the example of constructing an adiabatic DANTE inversion pulse. This new adiabatic pulse is the first narrow band selective adiabatic pulses: Adiabatic homonuclear and heteronuclear spectral editing sequences. Unique to the first pulse sequence is a B 1 -field filter which is built by using two non-refocusing adiabatic full passage pulses to refocus the wanted signal and dephase unwanted signals. This extra filter greatly enhance the editing efficiency. Unlike commonly used heteronuclear spectral editing sequences which depend on the polarization transfer or spectral subtraction by phase cycling techniques, the second pulse sequences accomplishes the editing of heteronuclear J-coupled signals based on the fact that this sequence is transparent to the uncoupled spins and is equivalent a 90 degrees excitation pulse to the heteronuclear J-coupled spins. Experimental results have confirmed the ability of spectral editing with these two new sequences
Directory of Open Access Journals (Sweden)
Rudowicz Czesław
2015-07-01
Full Text Available The interface between optical spectroscopy, electron magnetic resonance (EMR, and magnetism of transition ions forms the intricate web of interrelated notions. Major notions are the physical Hamiltonians, which include the crystal field (CF (or equivalently ligand field (LF Hamiltonians, and the effective spin Hamiltonians (SH, which include the zero-field splitting (ZFS Hamiltonians as well as to a certain extent also the notion of magnetic anisotropy (MA. Survey of recent literature has revealed that this interface, denoted CF (LF ↔ SH (ZFS, has become dangerously entangled over the years. The same notion is referred to by three names that are not synonymous: CF (LF, SH (ZFS, and MA. In view of the strong need for systematization of nomenclature aimed at bringing order to the multitude of different Hamiltonians and the associated quantities, we have embarked on this systematization. In this article, we do an overview of our efforts aimed at providing a deeper understanding of the major intricacies occurring at the CF (LF ↔ SH (ZFS interface with the focus on the EMR-related problems for transition ions.
Deformed fermion realization of the sp(4) algebra and its application
International Nuclear Information System (INIS)
Georgieva, A.I.; Sviratcheva, K.D.; Gueorguiev, V.G.; Draayer, J.P.
2002-01-01
Conclusions The deformed realization of sp_q(4) is based on the specific q-deformation of a two component Clifford algebra, realized in terms of creation and annihilation fermion operators. The deformed generators of Sp_q(4) close different realizations of the compact u_q(2) subalgebra. Each reduction into compact subalgebras of sp_q(4) provides for a description of a different physical model with different dynamical symmetries. While within a particular deformation scheme the basis states may either be deformed or not, the generators are always deformed as is their action on basis states. With a view towards applications, the additional parameter of the deformation gives in a Hamiltonian theory a dependence of the matrix elements on the q−deformation , which does not simply account for one more higher order of a two-body interaction, but it includes all of them through an exponential expansion in parameter κ, q = e"κ. In this way only one parameter, q, can restore the neglected non-linear terms of the residual interaction.
Adiabatic process reversibility: microscopic and macroscopic views
International Nuclear Information System (INIS)
Anacleto, Joaquim; Pereira, Mario G
2009-01-01
The reversibility of adiabatic processes was recently addressed by two publications. In the first (Miranda 2008 Eur. J. Phys. 29 937-43), an equation was derived relating the initial and final volumes and temperatures for adiabatic expansions of an ideal gas, using a microscopic approach. In that relation the parameter r accounts for the process reversibility, ranging between 0 and 1, which corresponds to the free and reversible expansion, respectively. In the second (Anacleto and Pereira 2009 Eur. J. Phys. 30 177-83), the authors have shown that thermodynamics can effectively and efficiently be used to obtain the general law for adiabatic processes carried out by an ideal gas, including compressions, for which r≥1. The present work integrates and extends the aforementioned studies, providing thus further insights into the analysis of the adiabatic process. It is shown that Miranda's work is wholly valid for compressions. In addition, it is demonstrated that the adiabatic reversibility coefficient given in terms of the piston velocity and the root mean square velocity of the gas particles is equivalent to the macroscopic description, given just by the quotient between surroundings and system pressure values. (letters and comments)
Derivation of Hamiltonians for accelerators
Energy Technology Data Exchange (ETDEWEB)
Symon, K.R.
1997-09-12
In this report various forms of the Hamiltonian for particle motion in an accelerator will be derived. Except where noted, the treatment will apply generally to linear and circular accelerators, storage rings, and beamlines. The generic term accelerator will be used to refer to any of these devices. The author will use the usual accelerator coordinate system, which will be introduced first, along with a list of handy formulas. He then starts from the general Hamiltonian for a particle in an electromagnetic field, using the accelerator coordinate system, with time t as independent variable. He switches to a form more convenient for most purposes using the distance s along the reference orbit as independent variable. In section 2, formulas will be derived for the vector potentials that describe the various lattice components. In sections 3, 4, and 5, special forms of the Hamiltonian will be derived for transverse horizontal and vertical motion, for longitudinal motion, and for synchrobetatron coupling of horizontal and longitudinal motions. Hamiltonians will be expanded to fourth order in the variables.
Relativistic non-Hamiltonian mechanics
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2010-01-01
Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.
Non-adiabatic description of proton emission from the odd-odd nucleus 130Eu
Directory of Open Access Journals (Sweden)
Patial Monika
2014-03-01
Full Text Available We discuss the non-adiabatic quasiparticle approach for calculating the rotational spectra and decay width of odd-odd proton emitters. The Coriolis effects are incorporated in both the parent and daughter wave functions. Results for the two probable ground states (1+ and 2+ of the proton emitter 130Eu are discussed. With our calculations, we confirm the proton emitting state to be the Iπ = 1+ state, irrespective of the strength of the Coriolis interaction. This study provides us with an opportunity to look into the details of wave functions of deformed odd-odd nuclei to which the proton emission halflives are quite sensitive.
Chromatic roots and hamiltonian paths
DEFF Research Database (Denmark)
Thomassen, Carsten
2000-01-01
We present a new connection between colorings and hamiltonian paths: If the chromatic polynomial of a graph has a noninteger root less than or equal to t(n) = 2/3 + 1/3 (3)root (26 + 6 root (33)) + 1/3 (3)root (26 - 6 root (33)) = 1.29559.... then the graph has no hamiltonian path. This result...
Hamiltonian structure of the Lotka-Volterra equations
Nutku, Y.
1990-03-01
The Lotka-Volterra equations governing predator-prey relations are shown to admit Hamiltonian structure with respect to a generalized Poisson bracket. These equations provide an example of a system for which the naive criterion for the existence of Hamiltonian structure fails. We show further that there is a three-component generalization of the Lotka-Volterra equations which is a bi-Hamiltonian system.
Boson mapping and the microscopic collective nuclear Hamiltonian
International Nuclear Information System (INIS)
Dobes, J.; Ivanova, S.P.; Dzholos, R.V.; Pedrosa, R.
1990-01-01
Starting with the mapping of the quadrupole collective states in the fermion space onto the boson space, the fermion nuclear problem is transformed into the boson one. The boson images of the bifermion operators and of the fermion Hamiltonian are found. Recurrence relations are used to obtain approximately the norm matrix which appears in the boson-fermion mapping. The resulting boson Hamiltonian contains terms which go beyond the ordinary SU(6) symmetry Hamiltonian of the interacting boson model. Calculations, however, suggest that on the phenomenological level the differences between the mapped Hamiltonian and the SU(6) Hamiltonian are not too important. 18 refs.; 2 figs
Adiabatic logic future trend and system level perspective
Teichmann, Philip
2012-01-01
Adiabatic logic is a potential successor for static CMOS circuit design when it comes to ultra-low-power energy consumption. Future development like the evolutionary shrinking of the minimum feature size as well as revolutionary novel transistor concepts will change the gate level savings gained by adiabatic logic. In addition, the impact of worsening degradation effects has to be considered in the design of adiabatic circuits. The impact of the technology trends on the figures of merit of adiabatic logic, energy saving potential and optimum operating frequency, are investigated, as well as degradation related issues. Adiabatic logic benefits from future devices, is not susceptible to Hot Carrier Injection, and shows less impact of Bias Temperature Instability than static CMOS circuits. Major interest also lies on the efficient generation of the applied power-clock signal. This oscillating power supply can be used to save energy in short idle times by disconnecting circuits. An efficient way to generate the p...
On integrable Hamiltonians for higher spin XXZ chain
International Nuclear Information System (INIS)
Bytsko, Andrei G.
2003-01-01
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to (3/2) are given. Relations between Hamiltonians for some U q (sl 2 )-symmetric and U(1)-symmetric universal r-matrices are studied; their properties are investigated. A certain modification of the higher spin periodic chain Hamiltonian is shown to be an integrable U q (sl 2 )-symmetric Hamiltonian for an open chain
Meeds, E.; Leenders, R.; Welling, M.; Meila, M.; Heskes, T.
2015-01-01
Approximate Bayesian computation (ABC) is a powerful and elegant framework for performing inference in simulation-based models. However, due to the difficulty in scaling likelihood estimates, ABC remains useful for relatively lowdimensional problems. We introduce Hamiltonian ABC (HABC), a set of
Hamiltonian quantum simulation with bounded-strength controls
International Nuclear Information System (INIS)
Bookatz, Adam D; Wocjan, Pawel; Viola, Lorenza
2014-01-01
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed. (papers)
Energy Technology Data Exchange (ETDEWEB)
Alceanu-G, Pinho de; Picard, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1965-07-01
The odd-odd deformed nuclei are described as a rotator plus two odd nucleons moving in orbitals {omega}{sub p} and {omega}{sub n} of the deformed potential. We investigate the energies and wave functions of the various states of the ({omega}{sub p}, {omega}{sub n}) configurations by calculating and numerically diagonalizing the Hamiltonian matrix (with R.P.C. and residual interactions). The Gallagher-Mosskowski coupling rules ana the abnormal K equals 0 rotational bands are discussed. (authors) [French] Les noyaux impair-impairs deformes sont decrits comme un rotateur plus deux nucleons non apparies dans les orbites {omega}{sub p} et {omega}{sub n} du potentiel deforme. Nous etudions le spectre d'energie et les fonctions d'onde des configurations ({omega}{sub p}, {omega}{sub n}) en tenant compte de l'interaction particule-rotation et de la force residuelle entre les deux nucleons celibataires.
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
International Nuclear Information System (INIS)
Zhang Mingjiang; Fang Jianhui; Lu Kai; Pang Ting; Lin Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained. (general)
Mathematical Modeling of Constrained Hamiltonian Systems
Schaft, A.J. van der; Maschke, B.M.
1995-01-01
Network modelling of unconstrained energy conserving physical systems leads to an intrinsic generalized Hamiltonian formulation of the dynamics. Constrained energy conserving physical systems are directly modelled as implicit Hamiltonian systems with regard to a generalized Dirac structure on the
Lagrangian and Hamiltonian dynamics
Mann, Peter
2018-01-01
An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics, with a relaxed and self-contained setting. Lagrangian and Hamiltonian dynamics is the continuation of Newton's classical physics into new formalisms, each highlighting novel aspects of mechanics that gradually build in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts routed in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples, thoughtful and vibrant illustrations as well as an informal narrative and numerous fresh, modern and inter-disciplinary applications. The book contains some unusual topics for a classical mechanics textbook. Mo...
Noncanonical Hamiltonian mechanics
International Nuclear Information System (INIS)
Litteljohn, R.G.
1986-01-01
Noncanonical variables in Hamiltonian mechanics were first used by Lagrange in 1808. In spite of this, most work in Hamiltonian mechanics has been carried out in canonical variables, up to this day. One reason for this is that noncanonical coordinates are seldom needed for mechanical problems based on Lagrangians of the form L = T - V, where T is the kinetic energy and V is the potential energy. Of course, such Lagrangians arise naturally in celestial mechanics, and as a result they form the paradigms of nineteenth-century mechanics and have become enshrined in all the mechanics textbooks. Certain features of modern problems, however, lead to the use of noncanonical coordinates. Among these are issues of gauge invariance and singular Lagrange a Poisson structures. In addition, certain problems, like the flow of magnetic-field lines in physical space, are naturally formulated in terms of noncanonical coordinates. None of these features is present in the nineteenth-century paradigms of mechanics, but they do arise in problems involving particle motion in the presence of magnetic fields. For example, the motion of a particle in an electromagnetic wave is an important one in plasma physics, but the usual Hamiltonian formulation is gauge dependent. For this problem, noncanonical approaches based on Lagrangians in phase space lead to powerful computational techniques which are gauge invariant. In the limit of strong magnetic fields, particle motion becomes 'guiding-center motion'. Guiding-center motion is also best understood in terms of noncanonical coordinates. Finally the flow of magnetic-field lines through physical space is a Hamiltonian system which is best understood with noncanonical coordinates. No doubt many more systems will arise in the future for which these noncanonical techniques can be applied. (author)
Variational identities and Hamiltonian structures
International Nuclear Information System (INIS)
Ma Wenxiu
2010-01-01
This report is concerned with Hamiltonian structures of classical and super soliton hierarchies. In the classical case, basic tools are variational identities associated with continuous and discrete matrix spectral problems, targeted to soliton equations derived from zero curvature equations over general Lie algebras, both semisimple and non-semisimple. In the super case, a supertrace identity is presented for constructing Hamiltonian structures of super soliton equations associated with Lie superalgebras. We illustrate the general theories by the KdV hierarchy, the Volterra lattice hierarchy, the super AKNS hierarchy, and two hierarchies of dark KdV equations and dark Volterra lattices. The resulting Hamiltonian structures show the commutativity of each hierarchy discussed and thus the existence of infinitely many commuting symmetries and conservation laws.
Design of ternary clocked adiabatic static random access memory
International Nuclear Information System (INIS)
Wang Pengjun; Mei Fengna
2011-01-01
Based on multi-valued logic, adiabatic circuits and the structure of ternary static random access memory (SRAM), a design scheme of a novel ternary clocked adiabatic SRAM is presented. The scheme adopts bootstrapped NMOS transistors, and an address decoder, a storage cell and a sense amplifier are charged and discharged in the adiabatic way, so the charges stored in the large switch capacitance of word lines, bit lines and the address decoder can be effectively restored to achieve energy recovery during reading and writing of ternary signals. The PSPICE simulation results indicate that the ternary clocked adiabatic SRAM has a correct logic function and low power consumption. Compared with ternary conventional SRAM, the average power consumption of the ternary adiabatic SRAM saves up to 68% in the same conditions. (semiconductor integrated circuits)
Design of ternary clocked adiabatic static random access memory
Pengjun, Wang; Fengna, Mei
2011-10-01
Based on multi-valued logic, adiabatic circuits and the structure of ternary static random access memory (SRAM), a design scheme of a novel ternary clocked adiabatic SRAM is presented. The scheme adopts bootstrapped NMOS transistors, and an address decoder, a storage cell and a sense amplifier are charged and discharged in the adiabatic way, so the charges stored in the large switch capacitance of word lines, bit lines and the address decoder can be effectively restored to achieve energy recovery during reading and writing of ternary signals. The PSPICE simulation results indicate that the ternary clocked adiabatic SRAM has a correct logic function and low power consumption. Compared with ternary conventional SRAM, the average power consumption of the ternary adiabatic SRAM saves up to 68% in the same conditions.
Almost periodic Hamiltonians: an algebraic approach
International Nuclear Information System (INIS)
Bellissard, J.
1981-07-01
We develop, by analogy with the study of periodic potential, an algebraic theory for almost periodic hamiltonians, leading to a generalized Bloch theorem. This gives rise to results concerning the spectral measures of these operators in terms of those of the corresponding Bloch hamiltonians
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Pu, Jin; Jiang, Qing-Quan; Zu, Xiao-Tao
2017-05-01
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant I_adia = \\oint p_i dq_i introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.
Scattering theory for Stark Hamiltonians
International Nuclear Information System (INIS)
Jensen, Arne
1994-01-01
An introduction to the spectral and scattering theory for Schroedinger operators is given. An abstract short range scattering theory is developed. It is applied to perturbations of the Laplacian. Particular attention is paid to the study of Stark Hamiltonians. The main result is an explanation of the discrepancy between the classical and the quantum scattering theory for one-dimensional Stark Hamiltonians. (author). 47 refs
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Theoretical issues in quantum computing: Graph isomorphism, PageRank, and Hamiltonian determination
Rudinger, Kenneth Michael
This thesis explores several theoretical questions pertaining to quantum computing. First we examine several questions regarding multi-particle quantum random walk-based algorithms for the graph isomorphism problem. We find that there exists a non-trivial difference between continuous-time walks of one and two non-interacting particles as compared to non-interacting walks of three or more particles, in that the latter are able to distinguish many strongly regular graphs (SRGs), a class of graphs with many graph pairs that are difficult to distinguish. We demonstrate analytically where this distinguishing power comes from, and we show numerically that three-particle and four-particle non-interacting continuous-time walks can distinguish many pairs of strongly regular graphs. We additionally show that this distinguishing power, while it grows with particle number, is bounded, so that no continuous-time non-interacting walk of fixed particle number can distinguish all strongly regular graphs. We then investigate the relationship between continuous-time and discrete-time walks, in the context of the graph isomorphism problem. While it has been previously demonstrated numerically that discrete-time walks of non-interacting particles can distinguish some SRGs, we demonstrate where this distinguishing power comes from. We also show that while no continuous-time non-interacting walk of fixed particle number can distinguish SRGs, it remains a possibility that such a discrete-time walk could, leaving open the possibility of a non-trivial difference between discrete-time and continuous-time walks. The last piece of our work on graph isomorphism examines limitations on certain kinds of continuous-time walk-based algorithms for distinguishing graphs. We show that a very general class of continuous-time walk algorithms, with a broad class of allowable interactions, cannot distinguish all graphs. We next consider a previously-proposed quantum adiabatic algorithm for computing the
Hartree-Fock calculations for strongly deformed and highly excited nuclei using the Skyrme force
International Nuclear Information System (INIS)
Zint, P.G.
1975-01-01
It has been shown that in CHF-calculations the Skyrme-force is usefull to describe strongly deformed nuclei with even proton and neutron number till separation. Thereby the eigenfunctions of the two-centre Hamiltonian form an adequate basis. With this procedure, we obtain the correct deformation of the 32 S-system. Induding the spurious energy of relative motion between the 16 O-fragments, the energy curve is a good approximation for the real potential, extracted form scattering experiments. (orig./WL) [de
Dynamical decoupling of unbounded Hamiltonians
Arenz, Christian; Burgarth, Daniel; Facchi, Paolo; Hillier, Robin
2018-03-01
We investigate the possibility to suppress interactions between a finite dimensional system and an infinite dimensional environment through a fast sequence of unitary kicks on the finite dimensional system. This method, called dynamical decoupling, is known to work for bounded interactions, but physical environments such as bosonic heat baths are usually modeled with unbounded interactions; hence, here, we initiate a systematic study of dynamical decoupling for unbounded operators. We develop a sufficient decoupling criterion for arbitrary Hamiltonians and a necessary decoupling criterion for semibounded Hamiltonians. We give examples for unbounded Hamiltonians where decoupling works and the limiting evolution as well as the convergence speed can be explicitly computed. We show that decoupling does not always work for unbounded interactions and we provide both physically and mathematically motivated examples.
Matchings Extend to Hamiltonian Cycles in 5-Cube
Directory of Open Access Journals (Sweden)
Wang Fan
2018-02-01
Full Text Available Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Energy Technology Data Exchange (ETDEWEB)
Hu, Dao-chun [College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); College of Mechanical and Electrical Engineering, Taizhou Vocational & Technical College, Taizhou 318000 (China); Chen, Ming-he, E-mail: meemhchen@nuaa.edu.cn [College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Wang, Lei; Cheng, Hu [College of Mechanical Engineering, Taizhou University, Taizhou 318000 (China)
2016-01-01
High speed stamping process is used to high strength and high electrical conductivity phosphor bronze with extremely high strain rates more than 10{sup 3} s{sup −1}. This study on the dynamic tensile behaviour and deformational mechanism is to optimise the high speed stamping processes and improve geometrical precision in finished products. Thus, the tensile properties and deformation behaviour of C5191 phosphor bronze under quasi-static tensile condition at a strain rate of 0.001 s{sup −1} by electronic universal testing machine, and dynamic tensile condition at strain rate of 500, 1000 and 1500 s{sup −1} by split Hopkinson tensile bar (SHTB) apparatus were studied. The effects of strain rate and the deformation mechanism were investigated by means of SEM and TEM. The results showed that the yield strength and tensile strength of C5191 phosphor bronze under high strain rates deformation increased by 32.77% and 11.07% respectively compared with quasi-static condition, the strain hardening index increases from 0.075 to 0.251, and the strength of the material strain rates sensitivity index change from 0.005 to 0.022, which presented a clear sensitive to strain rates. Therefore, it is claimed that the dominant deformation mechanism was changed by the dislocation motion under different strain rates, and the ability of plastic deformation of C5191 phosphor bronze increased due to the number of movable dislocations increased significantly, started multi-line slip, and the soft effect of adiabatic temperature rise at the strain rate ranging from 500 to 1500 s{sup −1}.
Hamiltonian Approach to 2+1 Dimensional Gravity
Cantini, L.; Menotti, P.; Seminara, D.
2002-12-01
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge has hamiltonian form. We give the exact diffeomorphism which transforms the spinning cone metric in the Deser, Jackiw, 't Hooft gauge to the maximally slicing gauge. It is explicitly shown that the boundary term in the action, written in hamiltonian form gives the hamiltonian for the reduced particle dynamics. The quantum mechanical translation of the two particle hamiltonian gives rise to the logarithm of the Laplace-Beltrami operator on a cone whose angular deficit is given by the total energy of the system irrespective of the masses of the particles thus proving at the quantum level a conjecture by 't Hooft on the two particle dynamics.
A Direct Method of Hamiltonian Structure
International Nuclear Information System (INIS)
Li Qi; Chen Dengyuan; Su Shuhua
2011-01-01
A direct method of constructing the Hamiltonian structure of the soliton hierarchy with self-consistent sources is proposed through computing the functional derivative under some constraints. The Hamiltonian functional is related with the conservation densities of the corresponding hierarchy. Three examples and their two reductions are given. (general)
On Distributed Port-Hamiltonian Process Systems
Lopezlena, Ricardo; Scherpen, Jacquelien M.A.
2004-01-01
In this paper we use the term distributed port-Hamiltonian Process Systems (DPHPS) to refer to the result of merging the theory of distributed Port-Hamiltonian systems (DPHS) with the theory of process systems (PS). Such concept is useful for combining the systematic interconnection of PHS with the
Plasma heating by adiabatic compression
International Nuclear Information System (INIS)
Ellis, R.A. Jr.
1972-01-01
These two lectures will cover the following three topics: (i) The application of adiabatic compression to toroidal devices is reviewed. The special case of adiabatic compression in tokamaks is considered in more detail, including a discussion of the equilibrium, scaling laws, and heating effects. (ii) The ATC (Adiabatic Toroidal Compressor) device which was completed in May 1972, is described in detail. Compression of a tokamak plasma across a static toroidal field is studied in this device. The device is designed to produce a pre-compression plasma with a major radius of 17 cm, toroidal field of 20 kG, and current of 90 kA. The compression leads to a plasma with major radius of 38 cm and minor radius of 10 cm. Scaling laws imply a density increase of a factor 6, temperature increase of a factor 3, and current increase of a factor 2.4. An additional feature of ATC is that it is a large tokamak which operates without a copper shell. (iii) Data which show that the expected MHD behavior is largely observed is presented and discussed. (U.S.)
A diagrammatic construction of formal E-independent model hamiltonian
International Nuclear Information System (INIS)
Kvasnicka, V.
1977-01-01
A diagrammatic construction of formal E-independent model interaction (i.e., without second-quantization formalism) is suggested. The construction starts from the quasi-degenerate Brillouin-Wigner perturbation theory, in the framework of which an E-dependent model Hamiltonian is simply constructed. Applying the ''E-removing'' procedure to this E-dependent model Hamiltonian, the E-independent formal model Hamiltonian either Hermitian or non-Hermitian can diagrammatically be easily derived. For the formal E-independent model Hamiltonian the separability theorem is proved, which can be profitably used for a rather ''formalistic ''construction of a many-body E-independent model Hamiltonian
Xie, Changjian; Malbon, Christopher L; Yarkony, David R; Guo, Hua
2017-07-28
The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S 1 state of phenol, which is affected by a C s symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI.
A new class of integrable deformations of CFTs
International Nuclear Information System (INIS)
Georgiou, George; Sfetsos, Konstantinos
2017-01-01
We construct a new class of integrable σ-models based on current algebra theories for a general semisimple group G by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two independent WZW models for G both at level k, perturbed by current bilinears mixing the different WZW models. A non-perturbative symmetry in the couplings parametric space is revealed. We perform the Hamiltonian analysis of the action and demonstrate integrability in several cases. We extend our construction to deformations of G/H CFTs and show integrability when G/H is a symmetric space. Our method resembles that used for constructing the λ-deformed integrable σ-models, but the results are distinct and novel.
A new class of integrable deformations of CFTs
Energy Technology Data Exchange (ETDEWEB)
Georgiou, George [Institute of Nuclear and Particle Physics, National Center for Scientific Research Demokritos, Ag. Paraskevi, GR-15310 Athens (Greece); Sfetsos, Konstantinos [Department of Nuclear and Particle Physics, Faculty of Physics, National and Kapodistrian University of Athens, Athens 15784 (Greece)
2017-03-15
We construct a new class of integrable σ-models based on current algebra theories for a general semisimple group G by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two independent WZW models for G both at level k, perturbed by current bilinears mixing the different WZW models. A non-perturbative symmetry in the couplings parametric space is revealed. We perform the Hamiltonian analysis of the action and demonstrate integrability in several cases. We extend our construction to deformations of G/H CFTs and show integrability when G/H is a symmetric space. Our method resembles that used for constructing the λ-deformed integrable σ-models, but the results are distinct and novel.
Port Hamiltonian modeling of Power Networks
van Schaik, F.; van der Schaft, Abraham; Scherpen, Jacquelien M.A.; Zonetti, Daniele; Ortega, R
2012-01-01
In this talk a full nonlinear model for the power network in port–Hamiltonian framework is derived to study its stability properties. For this we use the modularity approach i.e., we first derive the models of individual components in power network as port-Hamiltonian systems and then we combine all
Hamiltonian Cycles on Random Eulerian Triangulations
DEFF Research Database (Denmark)
Guitter, E.; Kristjansen, C.; Nielsen, Jakob Langgaard
1998-01-01
. Considering the case n -> 0, this implies that the system of random Eulerian triangulations equipped with Hamiltonian cycles describes a c=-1 matter field coupled to 2D quantum gravity as opposed to the system of usual random triangulations equipped with Hamiltonian cycles which has c=-2. Hence, in this case...
Semi adiabatic theory of seasonal Markov processes
Energy Technology Data Exchange (ETDEWEB)
Talkner, P [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Pu, Jin [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Jiang, Qing-Quan [China West Normal University, College of Physics and Space Science, Nanchong (China)
2017-05-15
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painleve) of coordinates as well as in different gravity frames, the adiabatic invariant I{sub adia} = circular integral p{sub i}dq{sub i} introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area. (orig.)
Incomplete Dirac reduction of constrained Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Chandre, C., E-mail: chandre@cpt.univ-mrs.fr
2015-10-15
First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.
Spectral and resonance properties of the Smilansky Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Exner, Pavel [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague (Czech Republic); Lotoreichik, Vladimir [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic); Tater, Miloš, E-mail: tater@ujf.cas.cz [Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague (Czech Republic)
2017-02-26
We analyze the Hamiltonian proposed by Smilansky to describe irreversible dynamics in quantum graphs and studied further by Solomyak and others. We derive a weak-coupling asymptotics of the ground state and add new insights by finding the discrete spectrum numerically in the subcritical case. Furthermore, we show that the model then has a rich resonance structure. - Highlights: • We derive conditions on bound states and on resonances of the Smilansky Hamiltonian. • Using these conditions we find numerically discrete spectrum and resonances of this Hamiltonian. • Our numerical tests confirm known properties of the Hamiltonian and allow us to conjecture new ones.
Adiabatic quantum search algorithm for structured problems
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
Pang, Shengshi; Jordan, Andrew N.
2017-01-01
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. PMID:28276428
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians.
Pang, Shengshi; Jordan, Andrew N
2017-03-09
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T 2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T 4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.
Hamiltonian representation of divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1984-11-01
Globally divergence-free fields, such as the magnetic field and the vorticity, can be described by a two degree of freedom Hamiltonian. The Hamiltonian function provides a complete topological description of the field lines. The formulation also separates the dissipative and inertial time scale evolution of the magnetic and the vorticity fields
Integrable N dimensional systems on the Hopf algebra and q deformations
International Nuclear Information System (INIS)
Lisitsyn, Ya.V.; Shapovalov, A.V.
2000-01-01
The class of integrable classic and quantum systems on the Hopf algebra, describing the n of interacting particles, is plotted. The general structure of the integrable Hamiltonian system for the Hopf algebra A(g) of the Lee simple algebra g is obtained, wherefrom it follows, that motion integrals depend on the linear combinations k of the phase space coordinates. The q-deformation standard procedure is carried out and the corresponding integrable system is obtained. The general scheme is illustrated by the examples of the sl(2), sl(3) and o(3, 1) algebras. The exact solution is achieved for the N-dimensional Hamiltonian system quantum analog on the Hopf algebra A (sl(2)) through the method of noncommutative integration of linear differential equations [ru
Hamiltonian structures of some non-linear evolution equations
International Nuclear Information System (INIS)
Tu, G.Z.
1983-06-01
The Hamiltonian structure of the O(2,1) non-linear sigma model, generalized AKNS equations, are discussed. By reducing the O(2,1) non-linear sigma model to its Hamiltonian form some new conservation laws are derived. A new hierarchy of non-linear evolution equations is proposed and shown to be generalized Hamiltonian equations with an infinite number of conservation laws. (author)
Numerical determination of the magnetic field line Hamiltonian
International Nuclear Information System (INIS)
Kuo-Petravic, G.; Boozer, A.H.
1986-03-01
The structure of a magnetic field is determined by a one-degree of freedom, time-dependent Hamiltonian. This Hamiltonian is evaluated for a given field in a perturbed action-angle form. The location and the size of magnetic islands in the given field are determined from Hamiltonian perturbation theory and from an ordinary Poincare plot of the field line trajectories
Hamiltonian analysis of transverse dynamics in axisymmetric rf photoinjectors
International Nuclear Information System (INIS)
Wang, C.-x.
2006-01-01
A general Hamiltonian that governs the beam dynamics in an rf photoinjector is derived from first principles. With proper choice of coordinates, the resulting Hamiltonian has a simple and familiar form, while taking into account the rapid acceleration, rf focusing, magnetic focusing, and space-charge forces. From the linear Hamiltonian, beam-envelope evolution is readily obtained, which better illuminates the theory of emittance compensation. Preliminary results on the third-order nonlinear Hamiltonian will be given as well.
Frustration-free Hamiltonians supporting Majorana zero edge modes
International Nuclear Information System (INIS)
Jevtic, Sania; Barnett, Ryan
2017-01-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs. (paper)
Frustration-free Hamiltonians supporting Majorana zero edge modes
Jevtic, Sania; Barnett, Ryan
2017-10-01
A one-dimensional fermionic system, such as a superconducting wire, may host Majorana zero-energy edge modes (MZMs) at its edges when it is in the topological phase. MZMs provide a path to realising fault-tolerant quantum computation, and so are the focus of intense experimental and theoretical studies. However, given a Hamiltonian, determining whether MZMs exist is a daunting task as it relies on knowing the spectral properties of the Hamiltonian in the thermodynamic limit. The Kitaev chain is a paradigmatic non-interacting model that supports MZMs and the Hamiltonian can be fully diagonalised. However, for interacting models, the situation is far more complex. Here we consider a different classification of models, namely, ones with frustration-free Hamiltonians. Within this class of models, interacting and non-interacting systems are treated on an equal footing, and we identify exactly which Hamiltonians can realise MZMs.
A parcel formulation for Hamiltonian layer models
Bokhove, Onno; Oliver, M.
Starting from the three-dimensional hydrostatic primitive equations, we derive Hamiltonian N-layer models with isentropic tropospheric and isentropic or isothermal stratospheric layers. Our construction employs a new parcel Hamiltonian formulation which describes the fluid as a continuum of
Block diagrams and the cancellation of divergencies in energy-level perturbation theory
International Nuclear Information System (INIS)
Michels, M.A.J.; Suttorp, L.G.
1979-01-01
The effective Hamiltonian for the degenerate energy-eigenvalue problem in adiabatic perturbation theory is cast in a form that permits an expansion in Feynman diagrams. By means of a block representation a resummation of these diagrams is carried out such that in the adiabatic limit no divergencies are encountered. The resummed form of the effective Hamiltonian is used to establish a connexion with the S matrix. (Auth.)
Are the reactions of quinones on graphite adiabatic?
International Nuclear Information System (INIS)
Luque, N.B.; Schmickler, W.
2013-01-01
Outer sphere electron transfer reactions on pure metal electrodes are often adiabatic and hence independent of the electrode material. Since it is not clear, whether adiabatic electron transfer can also occur on a semi-metal like graphite, we have re-investigated experimental data presented in a recent communication by Nissim et al. [Chemical Communications 48 (2012) 3294] on the reactions of quinones on graphite. We have supplemented their work by DFT calculations and conclude, that these reactions are indeed adiabatic. This contradicts the assertion of Nissim et al. that the rates are proportional to the density of states at the Fermi level
Effective Hamiltonians in quantum physics: resonances and geometric phase
International Nuclear Information System (INIS)
Rau, A R P; Uskov, D
2006-01-01
Effective Hamiltonians are often used in quantum physics, both in time-dependent and time-independent contexts. Analogies are drawn between the two usages, the discussion framed particularly for the geometric phase of a time-dependent Hamiltonian and for resonances as stationary states of a time-independent Hamiltonian
Improving the positive feedback adiabatic logic familiy
Directory of Open Access Journals (Sweden)
J. Fischer
2004-01-01
Full Text Available Positive Feedback Adiabatic Logic (PFAL shows the lowest energy dissipation among adiabatic logic families based on cross-coupled transistors, due to the reduction of both adiabatic and non-adiabatic losses. The dissipation primarily depends on the resistance of the charging path, which consists of a single p-channel MOSFET during the recovery phase. In this paper, a new logic family called Improved PFAL (IPFAL is proposed, where all n- and pchannel devices are swapped so that the charge can be recovered through an n-channel MOSFET. This allows to decrease the resistance of the charging path up to a factor of 2, and it enables a significant reduction of the energy dissipation. Simulations based on a 0.13µm CMOS process confirm the improvements in terms of power consumption over a large frequency range. However, the same simple design rule, which enables in PFAL an additional reduction of the dissipation by optimal transistor sizing, does not apply to IPFAL. Therefore, the influence of several sources of dissipation for a generic IPFAL gate is illustrated and discussed, in order to lower the power consumption and achieve better performance.
Adiabatic invariants of the extended KdV equation
Energy Technology Data Exchange (ETDEWEB)
Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)
2017-01-30
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.
A generalized AKNS hierarchy and its bi-Hamiltonian structures
International Nuclear Information System (INIS)
Xia Tiecheng; You Fucai; Chen Dengyuan
2005-01-01
First we construct a new isospectral problem with 8 potentials in the present paper. And then a new Lax pair is presented. By making use of Tu scheme, a class of new soliton hierarchy of equations is derived, which is integrable in the sense of Liouville and possesses bi-Hamiltonian structures. After making some reductions, the well-known AKNS hierarchy and other hierarchies of evolution equations are obtained. Finally, in order to illustrate that soliton hierarchy obtained in the paper possesses bi-Hamiltonian structures exactly, we prove that the linear combination of two-Hamiltonian operators admitted are also a Hamiltonian operator constantly. We point out that two Hamiltonian operators obtained of the system are directly derived from a recurrence relations, not from a recurrence operator
Gravitational surface Hamiltonian and entropy quantization
Directory of Open Access Journals (Sweden)
Ashish Bakshi
2017-02-01
Full Text Available The surface Hamiltonian corresponding to the surface part of a gravitational action has xp structure where p is conjugate momentum of x. Moreover, it leads to TS on the horizon of a black hole. Here T and S are temperature and entropy of the horizon. Imposing the hermiticity condition we quantize this Hamiltonian. This leads to an equidistant spectrum of its eigenvalues. Using this we show that the entropy of the horizon is quantized. This analysis holds for any order of Lanczos–Lovelock gravity. For general relativity, the area spectrum is consistent with Bekenstein's observation. This provides a more robust confirmation of this earlier result as the calculation is based on the direct quantization of the Hamiltonian in the sense of usual quantum mechanics.
First principles of Hamiltonian medicine.
Crespi, Bernard; Foster, Kevin; Úbeda, Francisco
2014-05-19
We introduce the field of Hamiltonian medicine, which centres on the roles of genetic relatedness in human health and disease. Hamiltonian medicine represents the application of basic social-evolution theory, for interactions involving kinship, to core issues in medicine such as pathogens, cancer, optimal growth and mental illness. It encompasses three domains, which involve conflict and cooperation between: (i) microbes or cancer cells, within humans, (ii) genes expressed in humans, (iii) human individuals. A set of six core principles, based on these domains and their interfaces, serves to conceptually organize the field, and contextualize illustrative examples. The primary usefulness of Hamiltonian medicine is that, like Darwinian medicine more generally, it provides novel insights into what data will be productive to collect, to address important clinical and public health problems. Our synthesis of this nascent field is intended predominantly for evolutionary and behavioural biologists who aspire to address questions directly relevant to human health and disease.
Adiabatic burst evaporation from bicontinuous nanoporous membranes
Ichilmann, Sachar; Rücker, Kerstin; Haase, Markus; Enke, Dirk
2015-01-01
Evaporation of volatile liquids from nanoporous media with bicontinuous morphology and pore diameters of a few 10 nm is an ubiquitous process. For example, such drying processes occur during syntheses of nanoporous materials by sol–gel chemistry or by spinodal decomposition in the presence of solvents as well as during solution impregnation of nanoporous hosts with functional guests. It is commonly assumed that drying is endothermic and driven by non-equilibrium partial pressures of the evaporating species in the gas phase. We show that nearly half of the liquid evaporates in an adiabatic mode involving burst-like liquid-to-gas conversions. During single adiabatic burst evaporation events liquid volumes of up to 107 μm3 are converted to gas. The adiabatic liquid-to-gas conversions occur if air invasion fronts get unstable because of the built-up of high capillary pressures. Adiabatic evaporation bursts propagate avalanche-like through the nanopore systems until the air invasion fronts have reached new stable configurations. Adiabatic cavitation bursts thus compete with Haines jumps involving air invasion front relaxation by local liquid flow without enhanced mass transport out of the nanoporous medium and prevail if the mean pore diameter is in the range of a few 10 nm. The results reported here may help optimize membrane preparation via solvent-based approaches, solution-loading of nanopore systems with guest materials as well as routine use of nanoporous membranes with bicontinuous morphology and may contribute to better understanding of adsorption/desorption processes in nanoporous media. PMID:25926406
Off-center Jahn-Teller ion: coupled polar and tetragonal deformations
International Nuclear Information System (INIS)
Vikhnin, V.S.; Sochava, L.S.
1979-01-01
Models of the off-center Jahn-Teller ions are considered, i.e. Ni + in SrO and Cu 27 in SrO studied earlier. Models of the off-center Jahn-Teller ion are proposed, in which mutual effect of dipole-active deformations conditioning off-centering and the Jahn-Teller tetragonal deformations takes place. Manifestations of a new type of multipit potential XY 24 of an off-center ion are considered. The Jahn-Teller effect (JTE) is studied for a duplicate in cubic environment, unharmonism of the fourth order being taken into account. In such a model of Exe of JTE, the position and quantity of minima of adiabatic potential are changed as compared with Exe of JTE taking account of unharmonism of the third order or the square Jahn-Teller interaction. While using models of the off-center Jahn-Teller ion which take account of the effect of two tetragonal Jahn-Teller deformations occurring in the Exe problem considering unharmonism of the fourth order produced on dipole-active deformations, it becomes possible to explain the experiment for SrO:Ni +
Adiabatic compression of elongated field-reversed configurations
International Nuclear Information System (INIS)
Spencer, R.L.; Tuszewski, M.; Linford, R.K.
1983-01-01
The adiabatic compression of an elongated field-reversed configuration (FRC) is computed by using a one-dimensional approximation. The one-dimensional results are checked against a two-dimensional equilibrium code. For ratios of FRC separatrix length to separatrix radius greater than about ten, the one-dimensional results are accurate within 10%. To this accuracy, the adiabatic compression of FRC's can be described by simple analytic formulas
Quantum Statistical Operator and Classically Chaotic Hamiltonian ...
African Journals Online (AJOL)
Quantum Statistical Operator and Classically Chaotic Hamiltonian System. ... Journal of the Nigerian Association of Mathematical Physics ... In a Hamiltonian system von Neumann Statistical Operator is used to tease out the quantum consequence of (classical) chaos engendered by the nonlinear coupling of system to its ...
Model Hamiltonian Calculations of the Nonlinear Polarizabilities of Conjugated Molecules.
Risser, Steven Michael
This dissertation advances the theoretical knowledge of the nonlinear polarizabilities of conjugated molecules. The unifying feature of these molecules is an extended delocalized pi electron structure. The pi electrons dominate the electronic properties of the molecules, allowing prediction of molecular properties based on the treatment of just the pi electrons. Two separate pi electron Hamiltonians are used in the research. The principal Hamiltonian used is the non-interacting single-particle Huckel Hamiltonian, which replaces the Coulomb interaction among the pi electrons with a mean field interaction. The simplification allows for exact solution of the Hamiltonian for large molecules. The second Hamiltonian used for this research is the interacting multi-particle Pariser-Parr-Pople (PPP) Hamiltonian, which retains explicit Coulomb interactions. This limits exact solutions to molecules containing at most eight electrons. The molecular properties being investigated are the linear polarizability, and the second and third order hyperpolarizabilities. The hyperpolarizabilities determine the nonlinear optical response of materials. These molecular parameters are determined by two independent approaches. The results from the Huckel Hamiltonian are obtained through first, second and third order perturbation theory. The results from the PPP Hamiltonian are obtained by including the applied field directly in the Hamiltonian and determining the ground state energy at a series of field strengths. By fitting the energy to a polynomial in field strength, the polarizability and hyperpolarizabilities are determined. The Huckel Hamiltonian is used to calculate the third order hyperpolarizability of polyenes. These calculations were the first to show the average hyperpolarizability of the polyenes to be positive, and also to show the saturation of the hyperpolarizability. Comparison of these Huckel results to those from the PPP Hamiltonian shows the lack of explicit Coulomb
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
Dependence of adiabatic population transfer on pulse profile
Indian Academy of Sciences (India)
Control of population transfer by rapid adiabatic passage has been an established technique wherein the exact amplitude profile of the shaped pulse is considered to be insignificant. We study the effect of ultrafast shaped pulses for two-level systems, by density-matrix approach. However, we find that adiabaticity depends ...
International Nuclear Information System (INIS)
Buechner, J.M.
1989-01-01
For a number of problems in the Plasma Astrophysics it is necessary to know the laws, which govern the non adiabatic charged particle dynamics in strongly curves magnetic field reversals. These are, e.q., the kinetic theory of the microscopic and macroscopicstability of current sheets in collionless plasma, of microturbulence, causing anomalous resistivity and dissipating currents, the problem of spontaneous reconnection, the formation of non Maxwellian distribution functions, particle acceleration and the use of particles as a diagnostic tool ('tracers'). To find such laws we derived from the differential equations of motion discrete mappings. These mappings allow an investigation of the motion after the break down of the adiabaticity of the magnetic moment. (author). 32 refs.; 5 figs.; 1 tab
Recent developments in trapping and manipulation of atoms with adiabatic potentials
Garraway, Barry M.; Perrin, Hélène
2016-09-01
A combination of static and oscillating magnetic fields can be used to ‘dress’ atoms with radio-frequency (RF), or microwave, radiation. The spatial variation of these fields can be used to create an enormous variety of traps for ultra-cold atoms and quantum gases. This article reviews the type and character of these adiabatic traps and the applications which include atom interferometry and the study of low-dimensional quantum systems. We introduce the main concepts of magnetic traps leading to adiabatic dressed traps. The concept of adiabaticity is discussed in the context of the Landau-Zener model. The first bubble trap experiment is reviewed together with the method used for loading it. Experiments based on atom chips show the production of double wells and ring traps. Dressed atom traps can be evaporatively cooled with an additional RF field, and a weak RF field can be used to probe the spectroscopy of the adiabatic potentials. Several approaches to ring traps formed from adiabatic potentials are discussed, including those based on atom chips, time-averaged adiabatic potentials and induction methods. Several proposals for adiabatic lattices with dressed atoms are also reviewed.
Local Hamiltonians for maximally multipartite-entangled states
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-10-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Local Hamiltonians for maximally multipartite-entangled states
International Nuclear Information System (INIS)
Facchi, P.; Florio, G.; Pascazio, S.; Pepe, F.
2010-01-01
We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from 3 to 5) and show some example Hamiltonians with MMESs as eigenstates.
Muonic molecules as three-body Coulomb problem in adiabatic approximation
International Nuclear Information System (INIS)
Decker, M.
1994-04-01
The three-body Coulomb problem is treated within the framework of the hyperspherical adiabatic approach. The surface functions are expanded into Faddeev-type components in order to ensure the equivalent representation of all possible two-body contributions. It is shown that this decomposition reduces the numerical effort considerably. The remaining radial equations are solved both in the extreme and the uncoupled adiabatic approximation to determine the binding energies of the systems (dtμ) and (d 3 Heμ). Whereas the ground state is described very well in the uncoupled adiabatic approximation, the excited states should be treated within the coupled adiabatic approximation to obtain good agreement with variational calculations. (orig.)
Adiabatic compression of elongated field-reversed configurations
Energy Technology Data Exchange (ETDEWEB)
Spencer, R.L.; Tuszewski, M.; Linford, R.K.
1983-06-01
The adiabatic compression of an elongated field-reversed configuration (FRC) is computed by using a one-dimensional approximation. The one-dimensional results are checked against a two-dimensional equilibrium code. For ratios of FRC separatrix length to separatrix radius greater than about ten, the one-dimensional results are accurate within 10%. To this accuracy, the adiabatic compression of FRC's can be described by simple analytic formulas.
Greenberger-Horne-Zeilinger States and Few-Body Hamiltonians
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V.
2011-12-01
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Greenberger-Horne-Zeilinger states and few-body Hamiltonians.
Facchi, Paolo; Florio, Giuseppe; Pascazio, Saverio; Pepe, Francesco V
2011-12-23
The generation of Greenberger-Horne-Zeilinger (GHZ) states is a crucial problem in quantum information. We derive general conditions for obtaining GHZ states as eigenstates of a Hamiltonian. We find that a necessary condition for an n-qubit GHZ state to be a nondegenerate eigenstate of a Hamiltonian is the presence of m-qubit couplings with m≥[(n+1)/2]. Moreover, we introduce a Hamiltonian with a GHZ eigenstate and derive sufficient conditions for the removal of the degeneracy.
Effective Hamiltonian for travelling discrete breathers
MacKay, Robert S.; Sepulchre, Jacques-Alexandre
2002-05-01
Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.
Adiabatic Compression Sensitivity of AF-M315E
2015-07-01
Brand for their technical expertise and guidance. He also wishes to thank Mr. Stephen McKim from NASA Goddard Space Flight Center for his assistance...Wilson, D. B., and Stoltzfus, J. M. "Adiabatic Compression of Oxygen: Real Fluid Temperatures," 2000. 10Ismail, I. M. K., and Hawkins , T. W. "Adiabatic
Bountis, Tassos
2012-01-01
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) res...
Study of phase transition of even and odd nuclei based on q-deforme SU(1,1) algebraic model
Jafarizadeh, M. A.; Amiri, N.; Fouladi, N.; Ghapanvari, M.; Ranjbar, Z.
2018-04-01
The q-deformed Hamiltonian for the SO (6) ↔ U (5) transitional case in s, d interaction boson model (IBM) can be constructed by using affine SUq (1 , 1) Lie algebra in the both IBM-1 and 2 versions and IBFM. In this research paper, we have studied the energy spectra of 120-128Xe isotopes and 123-131Xe isotopes and B(E2) transition probabilities of 120-128Xe isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes of the theory of quantum deformation. The theoretical results agree with the experimental data fairly well. It is shown that the q-deformed SO (6) ↔ U (5) transitional dynamical symmetry remains after deformation.
Invariant metrics for Hamiltonian systems
International Nuclear Information System (INIS)
Rangarajan, G.; Dragt, A.J.; Neri, F.
1991-05-01
In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs
Excited collective states of nuclei within Bohr Hamiltonian with Tietz-Hua potential
Energy Technology Data Exchange (ETDEWEB)
Chabab, M.; El Batoul, A.; Lahbas, A.; Oulne, M. [Cadi Ayyad University, High Energy Physics and Astrophysics Laboratory, Faculty of Sciences Semlalia, Marrakesh (Morocco); Hamzavi, M. [University of Zanjan, Department of Physics, Zanjan (Iran, Islamic Republic of)
2017-07-15
In this paper, we present new analytical solutions of the Bohr Hamiltonian problem that we derived with the Tietz-Hua potential, here used for describing the β-part of the nuclear collective potential plus that of the harmonic oscillator for the γ-part. Also, we proceed to a systematic comparison of the numerical results obtained with this kind of β-potential with others which are widely used in such a framework as well as with the experiment. The calculations are carried out for energy spectra and electromagnetic transition probabilities for γ-unstable and axially symmetric deformed nuclei. In the same frame, we show the effect of the shape flatness of the β-potential beyond its minimum on transition rates calculations. (orig.)
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Momentum and hamiltonian in complex action theory
DEFF Research Database (Denmark)
Nagao, Keiichi; Nielsen, Holger Frits Bech
2012-01-01
$-parametrized wave function, which is a solution to an eigenvalue problem of a momentum operator $\\hat{p}$, in FPI with a starting Lagrangian. Solving the eigenvalue problem, we derive the momentum and Hamiltonian. Oppositely, starting from the Hamiltonian we derive the Lagrangian in FPI, and we are led...
International Nuclear Information System (INIS)
Zhang Yu-Feng; Muhammad, Iqbal; Yue Chao
2017-01-01
We extend two known dynamical systems obtained by Blaszak, et al. via choosing Casimir functions and utilizing Novikov–Lax equation so that a series of novel dynamical systems including generalized Burgers dynamical system, heat equation, and so on, are followed to be generated. Then we expand some differential operators presented in the paper to deduce two types of expanding dynamical models. By taking the generalized Burgers dynamical system as an example, we deform its expanding model to get a half-expanding system, whose recurrence operator is derived from Lax representation, and its Hamiltonian structure is also obtained by adopting a new way. Finally, we expand the generalized Burgers dynamical system to the (2+1)-dimensional case whose Hamiltonian structure is derived by Poisson tensor and gradient of the Casimir function. Besides, a kind of (2+1)-dimensional expanding dynamical model of the (2+1)-dimensional dynamical system is generated as well. (paper)
Integrable deformations of Lotka-Volterra systems
International Nuclear Information System (INIS)
Ballesteros, Angel; Blasco, Alfonso; Musso, Fabio
2011-01-01
The Hamiltonian structure of a class of three-dimensional (3D) Lotka-Volterra (LV) equations is revisited from a novel point of view by showing that the quadratic Poisson structure underlying its integrability structure is just a real three-dimensional Poisson-Lie group. As a consequence, the Poisson coalgebra map Δ (2) that is given by the group multiplication provides the keystone for the explicit construction of a new family of 3N-dimensional integrable systems that, under certain constraints, contain N sets of deformed versions of the 3D LV equations. Moreover, by considering the most generic Poisson-Lie structure on this group, a new two-parametric integrable perturbation of the 3D LV system through polynomial and rational perturbation terms is explicitly found. -- Highlights: → A new Poisson-Lie approach to the integrability of Lotka-Volterra system is given. → New integrable deformations of the 3D Lotka-Volterra system are obtained. → Integrable Lotka-Volterra-type equations in 3N dimensions are deduced.
Diffeomorphism invariance in the Hamiltonian formulation of General Relativity
International Nuclear Information System (INIS)
Kiriushcheva, N.; Kuzmin, S.V.; Racknor, C.; Valluri, S.R.
2008-01-01
It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity
An approach for obtaining integrable Hamiltonians from Poisson-commuting polynomial families
Leyvraz, F.
2017-07-01
We discuss a general approach permitting the identification of a broad class of sets of Poisson-commuting Hamiltonians, which are integrable in the sense of Liouville. It is shown that all such Hamiltonians can be solved explicitly by a separation of variables ansatz. The method leads in particular to a proof that the so-called "goldfish" Hamiltonian is maximally superintegrable and leads to an elementary identification of a full set of integrals of motion. The Hamiltonians in involution with the "goldfish" Hamiltonian are also explicitly integrated. New integrable Hamiltonians are identified, among which some have the property of being isochronous, that is, all their orbits have the same period. Finally, a peculiar structure is identified in the Poisson brackets between the elementary symmetric functions and the set of Hamiltonians commuting with the "goldfish" Hamiltonian: these can be expressed as products between elementary symmetric functions and Hamiltonians. The structure displays an invariance property with respect to one element and has both a symmetry and a closure property. The meaning of this structure is not altogether clear to the author, but it turns out to be a powerful tool.
Adiabatic and non-adiabatic electron oscillations in a static electric field
International Nuclear Information System (INIS)
Wahlberg, C.
1977-03-01
The influence of a static electric field on the oscillations of a one-dimensional stream of electrons is investigated. In the weak field limit the oscillations are adiabatic and mode coupling negligible, but becomes significant if the field is tronger. The latter effect is believed to be of importance for the stability of e.g. potential double layers
International Nuclear Information System (INIS)
Peggs, S.; Talman, R.
1987-01-01
As proton accelerators get larger, and include more magnets, the conventional tracking programs which simulate them run slower. The purpose of this paper is to describe a method, still under development, in which element-by-element tracking around one turn is replaced by a single man, which can be processed far faster. It is assumed for this method that a conventional program exists which can perform faithful tracking in the lattice under study for some hundreds of turns, with all lattice parameters held constant. An empirical map is then generated by comparison with the tracking program. A procedure has been outlined for determining an empirical Hamiltonian, which can represent motion through many nonlinear kicks, by taking data from a conventional tracking program. Though derived by an approximate method this Hamiltonian is analytic in form and can be subjected to further analysis of varying degrees of mathematical rigor. Even though the empirical procedure has only been described in one transverse dimension, there is good reason to hope that it can be extended to include two transverse dimensions, so that it can become a more practical tool in realistic cases
Effective hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Avramenko, V.I.; Blokhin, A.L.
1989-01-01
Within the microscopic version of the unitary collective model with the horizontal mixing the effective Hamiltonian for 18 O and 18 Ne nuclei is constructed. The algebraic structure of the Hamiltonian is compared to the familiar phenomenological ones with the SU(3)-mixing terms which describe the coupled rotational and vibrational spectra. The Hamiltonian, including central nuclear and Coulomb interaction, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries. 32 refs.; 2 figs.; 4 tabs
Homotopical Dynamics IV: Hopf invariants and hamiltonian flows
Cornea, Octavian
2001-01-01
In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a gradient flow of the hamiltonian function $f$ imply the existence of bounded orbits for the hamiltonian flow of $f$. Once the existence of bounded orbits is established, under favorable circumstances, application of the $C^{1}$-closing lemma leads to period...
Effective magnetic Hamiltonians
Czech Academy of Sciences Publication Activity Database
Drchal, Václav; Kudrnovský, Josef; Turek, I.
2013-01-01
Roč. 26, č. 5 (2013), s. 1997-2000 ISSN 1557-1939 R&D Projects: GA ČR GA202/09/0775 Institutional support: RVO:68378271 Keywords : effective magnetic Hamiltonian * ab initio * magnetic structure Subject RIV: BE - Theoretical Physics Impact factor: 0.930, year: 2013
Quasi-adiabatic Switching for Metal-Island Quantum-dot Cellular Automata
Toth, Geza; Lent, Craig S.
2000-01-01
Recent experiments have demonstrated a working cell suitable for implementing the Quantum-dot Cellular Automata (QCA) paradigm. These experiments have been performed using metal island clusters. The most promising approach to QCA operation involves quasi-adiabatically switching the cells. This has been analyzed extensively in gated semiconductor cells. Here we present a metal island cell structure that makes quasi-adiabatic switching possible. We show how this permits quasi-adiabatic clocking...
A local inverse spectral theorem for Hamiltonian systems
International Nuclear Information System (INIS)
Langer, Matthias; Woracek, Harald
2011-01-01
We consider (2 × 2)-Hamiltonian systems of the form y'(x) = zJH(x)y(x), x in [s − , s + ). If a system of this form is in the limit point case, an analytic function is associated with it, namely its Titchmarsh–Weyl coefficient q H . The (global) uniqueness theorem due to de Branges says that the Hamiltonian H is (up to reparameterization) uniquely determined by the function q H . In this paper we give a local uniqueness theorem; if the Titchmarsh–Weyl coefficients q H 1 and q H 2 corresponding to two Hamiltonian systems are exponentially close, then the Hamiltonians H 1 and H 2 coincide (up to reparameterization) up to a certain point of their domain, which depends on the quantitative degree of exponential closeness of the Titchmarsh–Weyl coefficients
Non-adiabatic effect on Laughlin's argument of the quantum Hall effect
International Nuclear Information System (INIS)
Maruyama, I; Hatsugai, Y
2009-01-01
We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a pumped charge is quantized, known as Laughlin's argument in a cylindrical lattice. In a uniform electric field, we obtained a formula connecting quantized pumping in the adiabatic limit and no-pumping in the sudden limit. The intermediate region between the two limits is determined by the Landau gap. A randomness or impurity effect is also discussed.
Contact symmetries and Hamiltonian thermodynamics
International Nuclear Information System (INIS)
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-01-01
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production
Generic Local Hamiltonians are Gapless
Movassagh, Ramis
2017-12-01
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded maximum vertex degree. The type of interactions allowed for include translational invariance in a disorder (i.e., probabilistic) sense with some assumptions on the local distributions. Examples include many-body localization and random spin models. We calculate the scaling of the gap with the system's size when the local terms are distributed according to a Gaussian β orthogonal random matrix ensemble. As a corollary, there exist finite size partitions with respect to which the ground state is arbitrarily close to a product state. When the local eigenvalue distribution is discrete, in addition to the lack of an energy gap in the limit, we prove that the ground state has finite size degeneracies. The proofs are simple and constructive. This work excludes the important class of truly translationally invariant Hamiltonians where the local terms are all equal.
Hamiltonian formulation for the Martin-Taylor model
International Nuclear Information System (INIS)
Vasconcelos, D.B.; Viana, R.L.
1993-01-01
Locally stochastic layer and its optimization are studied. In order to accomplish this task, it is employed a Hamiltonian formulation of magnetic field line flow with a subsequent application of Escande-Doveil renormalization method which have been extensively used to obtain accurate estimates of stochasticity thresholds in systems exhibiting Hamiltonian chaos. (author)
Hamiltonian structure of linearly extended Virasoro algebra
International Nuclear Information System (INIS)
Arakelyan, T.A.; Savvidi, G.K.
1991-01-01
The Hamiltonian structure of linearly extended Virasoro algebra which admits free bosonic field representation is described. An example of a non-trivial extension is found. The hierarchy of integrable non-linear equations corresponding to this Hamiltonian structure is constructed. This hierarchy admits the Lax representation by matrix Lax operator of second order
Remarks on Hamiltonian structures in G2-geometry
International Nuclear Information System (INIS)
Cho, Hyunjoo; Salur, Sema; Todd, A. J.
2013-01-01
In this article, we treat G 2 -geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G 2 -structure; in particular, we discuss existence and make a number of identifications of the spaces of Hamiltonian structures associated to the two multisymplectic structures associated to an integrable G 2 -structure. Along the way, we prove some results in multisymplectic geometry that are generalizations of results from symplectic geometry
Constraints on the Adiabatic Temperature Change in Magnetocaloric Materials
DEFF Research Database (Denmark)
Nielsen, Kaspar Kirstein; Bahl, Christian Robert Haffenden; Smith, Anders
2010-01-01
The thermodynamics of the magnetocaloric effect implies constraints on the allowed variation in the adiabatic temperature change for a magnetocaloric material. An inequality for the derivative of the adiabatic temperature change with respect to temperature is derived for both first- and second...
QCD string with quarks. 2. Light cone Hamiltonian
International Nuclear Information System (INIS)
Dubin, A.Yu.; Kaidalov, A.B.; Simonov, Yu.A.
1994-01-01
The light-cone Hamiltonian is derived from the general gauge - and Lorentz - invariant expression for the qq-bar Green function. The resulting Hamiltonian contains in a non-additive way contributions from quark and string degrees of freedom
Static and dynamic deformations of actinide nuclei
International Nuclear Information System (INIS)
Rozmej, P.
1985-09-01
The zero-point quadrupole-hexadecapole vibrations have been taken into account to calculate dynamical deformations for even-even actinide nuclei. The collective and intrinsic motions are separated according to the Born-Oppenheimer approximation. The collective Hamiltonian is constructed using the macroscopic-microscopic method in the potential energy part and the cranking model in the kinetic energy part. The BCS theory with a modified oscillator potential is applied to describe the intrinsic motion of nucleons. A new set of Nilsson potential parameters, which produces a much better description of the properties of light actinide nuclei, has also been found. (orig.)
Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces
Jacob, Birgit
2012-01-01
This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research. Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the fir
Modeling non-adiabatic photoexcited reaction dynamics in condensed phases
International Nuclear Information System (INIS)
Coker, D.F.
2003-01-01
Reactions of photoexcited molecules, ions, and radicals in condensed phase environments involve non-adiabatic dynamics over coupled electronic surfaces. We focus on how local environmental symmetries can effect non-adiabatic coupling between excited electronic states and thus influence, in a possibly controllable way, the outcome of photo-excited reactions. Semi-classical and mixed quantum-classical non-adiabatic molecular dynamics methods, together with semi-empirical excited state potentials are used to probe the dynamical mixing of electronic states in different environments from molecular clusters, to simple liquids and solids, and photo-excited reactions in complex reaction environments such as zeolites
A design study of non-adiabatic electron guns
International Nuclear Information System (INIS)
Barroso, J.J.; Stellati, C.
1994-01-01
The design of a non-adiabatic gun capable of producing a 10 A, 50 KeV high-quality laminar electron beam is reported. In contrast to the magnetron injection gun with a conical cathode, where the beam is generated initially with a transverse velocity component, in the non-adiabatic gun electrons are extracted in a direction parallel to the axial guide magnetic field. The beam electrons acquire cyclotron motion as result of non-adiabatic processes in a strong non uniform electric field across the modulation anode. Such an extraction method gives rise to favourable features that are explored throughout the work. An extensive numerical simulation study has also been done to minimize velocity and energy spreads. (author). 3 refs, 5 figs, 1 tab
Manukure, Solomon
2018-04-01
We construct finite-dimensional Hamiltonian systems by means of symmetry constraints from the Lax pairs and adjoint Lax pairs of a bi-Hamiltonian hierarchy of soliton equations associated with the 3-dimensional special linear Lie algebra, and discuss the Liouville integrability of these systems based on the existence of sufficiently many integrals of motion.
Adiabatic and isothermal resistivities
International Nuclear Information System (INIS)
Fishman, R.S.
1989-01-01
The force-balance method is used to calculate the isothermal resistivity to first order in the electric field. To lowest order in the impurity potential, the isothermal resistivity disagrees with the adiabatic results of the Kubo formula and the Boltzmann equation. However, an expansion of the isothermal resistivity in powers of the impurity potential is divergent, with two sets of divergent terms. The first set arises from the density matrix of the relative electron-phonon system. The second set arises from the explicit dependence of the density matrix on the electric field, which was ignored by force-balance calculations. These divergent contributions are calculated inductively, by applying a recursion relation for the Green's functions. Using the λ 2 t→∞ limit of van Hove, I show that the resummation of these divergent terms yields the same result for the resistivity as the adiabatic calculations, in direct analogy with the work of Argyres and Sigel, and Huberman and Chester
Combinatorial quantization of the Hamiltonian Chern-Simons theory
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Grosse, H.; Schomerus, V.
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of ''functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional ω (''integration''). We prove that this data does not depend on the particular choices which have been made in the construction. The algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group. (orig.). With 1 fig
Local modular Hamiltonians from the quantum null energy condition
Koeller, Jason; Leichenauer, Stefan; Levine, Adam; Shahbazi-Moghaddam, Arvin
2018-03-01
The vacuum modular Hamiltonian K of the Rindler wedge in any relativistic quantum field theory is given by the boost generator. Here we investigate the modular Hamiltonian for more general half-spaces which are bounded by an arbitrary smooth cut of a null plane. We derive a formula for the second derivative of the modular Hamiltonian with respect to the coordinates of the cut which schematically reads K''=Tv v . This formula can be integrated twice to obtain a simple expression for the modular Hamiltonian. The result naturally generalizes the standard expression for the Rindler modular Hamiltonian to this larger class of regions. Our primary assumptions are the quantum null energy condition—an inequality between the second derivative of the von Neumann entropy of a region and the stress tensor—and its saturation in the vacuum for these regions. We discuss the validity of these assumptions in free theories and holographic theories to all orders in 1 /N .
Periodic solutions of asymptotically linear Hamiltonian systems without twist conditions
Energy Technology Data Exchange (ETDEWEB)
Cheng Rong [Coll. of Mathematics and Physics, Nanjing Univ. of Information Science and Tech., Nanjing (China); Dept. of Mathematics, Southeast Univ., Nanjing (China); Zhang Dongfeng [Dept. of Mathematics, Southeast Univ., Nanjing (China)
2010-05-15
In dynamical system theory, especially in many fields of applications from mechanics, Hamiltonian systems play an important role, since many related equations in mechanics can be written in an Hamiltonian form. In this paper, we study the existence of periodic solutions for a class of Hamiltonian systems. By applying the Galerkin approximation method together with a result of critical point theory, we establish the existence of periodic solutions of asymptotically linear Hamiltonian systems without twist conditions. Twist conditions play crucial roles in the study of periodic solutions for asymptotically linear Hamiltonian systems. The lack of twist conditions brings some difficulty to the study. To the authors' knowledge, very little is known about the case, where twist conditions do not hold. (orig.)
On local Hamiltonians and dissipative systems
Energy Technology Data Exchange (ETDEWEB)
Castagnino, M. [CONICET-Institutos de Fisica Rosario y de Astronomia y Fisica del Espacio Casilla de Correos 67, Sucursal 28, 1428, Buenos Aires (Argentina); Gadella, M. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina) and Departamento de Fisica Teorica, Facultad de Ciencias c. Real de Burgos, s.n., 47011 Valladolid (Spain)]. E-mail: manuelgadella@yahoo.com.ar; Lara, L.P. [Facultad de Ciencias Exactas, Ingenieria y Agrimensura UNR, Rosario (Argentina)
2006-11-15
We study a type of one-dimensional dynamical systems on the corresponding two-dimensional phase space. By using arguments related to the existence of integrating factors for Pfaff equations, we show that some one-dimensional non-Hamiltonian systems like dissipative systems, admit a Hamiltonian description by sectors on the phase plane. This picture is not uniquely defined and is coordinate dependent. A simple example is exhaustively discussed. The method, is not always applicable to systems with higher dimensions.
International Nuclear Information System (INIS)
Molique, H.; Dudek, J.
1997-01-01
A particle-number conserving approach is presented to solve the nuclear mean-field plus pairing Hamiltonian problem with a realistic deformed Woods-Saxon single-particle potential. The method is designed for the state-dependent monopole pairing Hamiltonian H pair =summation αβ G αβ c α † c bar α † c bar β c β with an arbitrary set of matrix elements G αβ . Symmetries of the Hamiltonians on the many-body level are discussed using the language of P symmetry introduced earlier in the literature and are employed to diagonalize the problem; the only essential approximation used is a many-body (Fock-space) basis cutoff. An optimal basis construction is discussed and the stability of the final result with respect to the basis cutoff is illustrated in details. Extensions of the concept of P symmetry are introduced and their consequences for an optimal many-body basis cutoff construction are exploited. An algorithm is constructed allowing to solve the pairing problems in the many-body spaces corresponding to p∼40 particles on n∼80 levels and for several dozens of lowest lying states with precision ∼(1 endash 2) % within seconds of the CPU time on a CRAY computer. Among applications, the presence of the low-lying seniority s=0 solutions, that are usually poorly described in terms of the standard approximations (BCS, HFB), is discussed and demonstrated to play a role in the interpretation of the spectra of rotating nuclei. copyright 1997 The American Physical Society
Teleportation of an Unknown Atomic State via Adiabatic Passage
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We propose a scheme for teleporting an unknown atomic state via adiabatic passage. Taking advantage of adiabatic passage, the atom has no probability of being excited and thus the atomic spontaneous emission is suppressed.We also show that the fidelity can reach 1 under certain condition.
Residual gauge invariance of Hamiltonian lattice gauge theories
International Nuclear Information System (INIS)
Ryang, S.; Saito, T.; Shigemoto, K.
1984-01-01
The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)
Nonadiabatic exchange dynamics during adiabatic frequency sweeps.
Barbara, Thomas M
2016-04-01
A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging. Copyright © 2016 Elsevier Inc. All rights reserved.
Nested Sampling with Constrained Hamiltonian Monte Carlo
Betancourt, M. J.
2010-01-01
Nested sampling is a powerful approach to Bayesian inference ultimately limited by the computationally demanding task of sampling from a heavily constrained probability distribution. An effective algorithm in its own right, Hamiltonian Monte Carlo is readily adapted to efficiently sample from any smooth, constrained distribution. Utilizing this constrained Hamiltonian Monte Carlo, I introduce a general implementation of the nested sampling algorithm.
Intertwined Hamiltonians in two-dimensional curved spaces
International Nuclear Information System (INIS)
Aghababaei Samani, Keivan; Zarei, Mina
2005-01-01
The problem of intertwined Hamiltonians in two-dimensional curved spaces is investigated. Explicit results are obtained for Euclidean plane, Minkowski plane, Poincare half plane (AdS 2 ), de Sitter plane (dS 2 ), sphere, and torus. It is shown that the intertwining operator is related to the Killing vector fields and the isometry group of corresponding space. It is shown that the intertwined potentials are closely connected to the integral curves of the Killing vector fields. Two problems are considered as applications of the formalism presented in the paper. The first one is the problem of Hamiltonians with equispaced energy levels and the second one is the problem of Hamiltonians whose spectrum is like the spectrum of a free particle
Estimation of the adiabatic energy limit versus beta in Baseball II
International Nuclear Information System (INIS)
Foote, J.H.
1976-01-01
Several estimates of the adiabatic energy limit versus beta in Baseball II are summarized, and the calculational methods used to obtain them are described. Some estimates are based on analytic expressions; for others, particle orbits are calculated, magnetic-moment jumps are inspected, and adiabatic limits then derived. The results are sensitive to the assumed variation of the combined vacuum-plus-plasma magnetic field. The calculated adiabatic energy limit falls rapidly with beta, even for a gradual magnetic-field variation. If we assume a sharp depression in the axial profile of the combined magnetic field for a finite-beta plasma, the adiabatic limit can be further markedly reduced
Adiabatic passage and ensemble control of quantum systems
International Nuclear Information System (INIS)
Leghtas, Z; Sarlette, A; Rouchon, P
2011-01-01
This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol-chirped pulse-practised by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude-shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with unknown coupling strengths. These adiabatic control protocols are illustrated by simulations on a four-level ladder.
NLO renormalization in the Hamiltonian truncation
Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.
2017-09-01
Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.
Noncanonical Hamiltonian methods in plasma dynamics
International Nuclear Information System (INIS)
Kaufman, A.N.
1982-01-01
A Hamiltonian approach to plasma dynamics is described. The Poisson bracket of two observables g 1 and g 2 is given by using an antisymmetric tensor J, and must satisfy the Jacobi condition. The J can be obtained by elementary tensor analysis. The evolution in time of an observable g is given in terms of the Poisson bracket and a Hamiltonian H(Z). The guiding-center description of particle motion was presented by Littlejohn. The ponderomotive drift and force, the wave-induced oscillation-center velocity, and the gyrofrequency shift are obtained. The Lie transform yields the wave-induced increment to the gyromomentum. In the coulomb model for a Vlasov system, the dynamical variable is the Vlasov distribution f(z). The Hamiltonian functional and the Poisson bracket are obtained. The coupling of f(z) to the Maxwell field appears in the Poisson bracket. The evolution equation yields the Vlasov-Maxwell system. (Kato, T.)
Topological structures of adiabatic phase for multi-level quantum systems
International Nuclear Information System (INIS)
Liu Zhengxin; Zhou Xiaoting; Liu Xin; Liu Xiongjun; Chen Jingling
2007-01-01
The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) has a monopole structure, the curvature 2-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures
Equivalence of Lagrangian and Hamiltonian BRST quantizations
International Nuclear Information System (INIS)
Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.
1992-01-01
Two approaches to the quantization of gauge theories using BRST symmetry are widely used nowadays: the Lagrangian quantization, developed in (BV-quantization) and Hamiltonian quantization, formulated in (BFV-quantization). For all known examples of field theory (Yang-Mills theory, gravitation etc.) both schemes give equivalent results. However the equivalence of these approaches in general wasn't proved. The main obstacle in comparing of these formulations consists in the fact, that in Hamiltonian approach the number of ghost fields is equal to the number of all first-class constraints, while in the Lagrangian approach the number of ghosts is equal to the number of independent gauge symmetries, which is equal to the number of primary first-class constraints only. This paper is devoted to the proof of the equivalence of Lagrangian and Hamiltonian quantizations for the systems with first-class constraints only. This is achieved by a choice of special gauge in the Hamiltonian approach. It's shown, that after integration over redundant variables on the functional integral we come to effective action which is constructed according to rules for construction of the effective action in Lagrangian quantization scheme
Hamiltonian evolutions of twisted polygons in RPn
International Nuclear Information System (INIS)
Beffa, Gloria Marì; Wang, Jing Ping
2013-01-01
In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP n , and we use them to describe invariant evolutions of projective N-gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N-gon invariant evolutions and the Hamiltonian evolutions on the invariants of the flow. We prove that any Hamiltonian evolution is induced on invariants by an invariant evolution of N-gons—what we call a projective realization—and both evolutions are connected explicitly in a very simple way. Finally, we provide a completely integrable evolution (the Boussinesq lattice related to the lattice W 3 -algebra), its projective realization in RP 2 and its Hamiltonian pencil. We generalize both structures to n-dimensions and we prove that they are Poisson, defining explicitly the n-dimensional generalization of the planar evolution (a discretization of the W n -algebra). We prove that the generalization is completely integrable, and we also give its projective realization, which turns out to be very simple. (paper)
An algorithm for finding a similar subgraph of all Hamiltonian cycles
Wafdan, R.; Ihsan, M.; Suhaimi, D.
2018-01-01
This paper discusses an algorithm to find a similar subgraph called findSimSubG algorithm. A similar subgraph is a subgraph with a maximum number of edges, contains no isolated vertex and is contained in every Hamiltonian cycle of a Hamiltonian Graph. The algorithm runs only on Hamiltonian graphs with at least two Hamiltonian cycles. The algorithm works by examining whether the initial subgraph of the first Hamiltonian cycle is a subgraph of comparison graphs. If the initial subgraph is not in comparison graphs, the algorithm will remove edges and vertices of the initial subgraph that are not in comparison graphs. There are two main processes in the algorithm, changing Hamiltonian cycle into a cycle graph and removing edges and vertices of the initial subgraph that are not in comparison graphs. The findSimSubG algorithm can find the similar subgraph without using backtracking method. The similar subgraph cannot be found on certain graphs, such as an n-antiprism graph, complete bipartite graph, complete graph, 2n-crossed prism graph, n-crown graph, n-möbius ladder, prism graph, and wheel graph. The complexity of this algorithm is O(m|V|), where m is the number of Hamiltonian cycles and |V| is the number of vertices of a Hamiltonian graph.
Hamiltonian constraint in polymer parametrized field theory
International Nuclear Information System (INIS)
Laddha, Alok; Varadarajan, Madhavan
2011-01-01
Recently, a generally covariant reformulation of two-dimensional flat spacetime free scalar field theory known as parametrized field theory was quantized using loop quantum gravity (LQG) type ''polymer'' representations. Physical states were constructed, without intermediate regularization structures, by averaging over the group of gauge transformations generated by the constraints, the constraint algebra being a Lie algebra. We consider classically equivalent combinations of these constraints corresponding to a diffeomorphism and a Hamiltonian constraint, which, as in gravity, define a Dirac algebra. Our treatment of the quantum constraints parallels that of LQG and obtains the following results, expected to be of use in the construction of the quantum dynamics of LQG: (i) the (triangulated) Hamiltonian constraint acts only on vertices, its construction involves some of the same ambiguities as in LQG and its action on diffeomorphism invariant states admits a continuum limit, (ii) if the regulating holonomies are in representations tailored to the edge labels of the state, all previously obtained physical states lie in the kernel of the Hamiltonian constraint, (iii) the commutator of two (density weight 1) Hamiltonian constraints as well as the operator correspondent of their classical Poisson bracket converge to zero in the continuum limit defined by diffeomorphism invariant states, and vanish on the Lewandowski-Marolf habitat, (iv) the rescaled density 2 Hamiltonian constraints and their commutator are ill-defined on the Lewandowski-Marolf habitat despite the well-definedness of the operator correspondent of their classical Poisson bracket there, (v) there is a new habitat which supports a nontrivial representation of the Poisson-Lie algebra of density 2 constraints.
On Adiabatic Processes at the Elementary Particle Level
A, Michaud
2016-01-01
Analysis of adiabatic processes at the elementary particle level and of the manner in which they correlate with the principle of conservation of energy, the principle of least action and entropy. Analysis of the initial and irreversible adiabatic acceleration sequence of newly created elementary particles and its relation to these principles. Exploration of the consequences if this first initial acceleration sequence is not subject to the principle of conservation.
Naz, Rehana; Naeem, Imran
2018-03-01
The non-standard Hamiltonian system, also referred to as a partial Hamiltonian system in the literature, of the form {\\dot q^i} = {partial H}/{partial {p_i}},\\dot p^i = - {partial H}/{partial {q_i}} + {Γ ^i}(t,{q^i},{p_i}) appears widely in economics, physics, mechanics, and other fields. The non-standard (partial) Hamiltonian systems arise from physical Hamiltonian structures as well as from artificial Hamiltonian structures. We introduce the term `artificial Hamiltonian' for the Hamiltonian of a model having no physical structure. We provide here explicitly the notion of an artificial Hamiltonian for dynamical systems of ordinary differential equations (ODEs). Also, we show that every system of second-order ODEs can be expressed as a non-standard (partial) Hamiltonian system of first-order ODEs by introducing an artificial Hamiltonian. This notion of an artificial Hamiltonian gives a new way to solve dynamical systems of first-order ODEs and systems of second-order ODEs that can be expressed as a non-standard (partial) Hamiltonian system by using the known techniques applicable to the non-standard Hamiltonian systems. We employ the proposed notion to solve dynamical systems of first-order ODEs arising in epidemics.
Interplay between electric and magnetic effect in adiabatic polaritonic systems
Alabastri, Alessandro; Toma, Andrea; Liberale, Carlo; Chirumamilla, Manohar; Giugni, Andrea; De Angelis, Francesco De; Das, Gobind; Di Fabrizio, Enzo M.; Proietti Zaccaria, Remo
2013-01-01
We report on the possibility of realizing adiabatic compression of polaritonic wave on a metallic conical nano-structure through an oscillating electric potential (quasi dynamic regime). By comparing this result with an electromagnetic wave excitation, we were able to relate the classical lighting-rod effect to adiabatic compression. Furthermore, we show that while the magnetic contribution plays a marginal role in the formation of adiabatic compression, it provides a blue shift in the spectral region. In particular, magnetic permeability can be used as a free parameter for tuning the polaritonic resonances. The peculiar form of adiabatic compression is instead dictated by both the source and the metal permittivity. The analysis is performed by starting from a simple electrostatic system to end with the complete electromagnetic one through intermediate situations such as the quasi-electrostatic and quasi-dynamic regimes. Each configuration is defined by a particular set of equations which allows to clearly determine the individual role played by the electric and magnetic contribution in the generation of adiabatic compression. We notice that these findings can be applied for the realization of a THz nano-metric generator. © 2013 Optical Society of America.
Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure
Jurčišinová, E.; Jurčišin, M.
2017-11-01
We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.
Modelling chaotic Hamiltonian systems as a Markov Chain ...
African Journals Online (AJOL)
The behaviour of chaotic Hamiltonian system has been characterised qualitatively in recent times by its appearance on the Poincaré section and quantitatively by the Lyapunov exponent. Studying the dynamics of the two chaotic Hamiltonian systems: the Henon-Heiles system and non-linearly coupled oscillators as their ...
Non-self-adjoint hamiltonians defined by Riesz bases
Energy Technology Data Exchange (ETDEWEB)
Bagarello, F., E-mail: fabio.bagarello@unipa.it [Dipartimento di Energia, Ingegneria dell' Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy); Inoue, A., E-mail: a-inoue@fukuoka-u.ac.jp [Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan); Trapani, C., E-mail: camillo.trapani@unipa.it [Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)
2014-03-15
We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, we give conditions under which these Hamiltonians can be factorized in terms of generalized lowering and raising operators.
Classical and quantum mechanics of complex Hamiltonian systems ...
Indian Academy of Sciences (India)
Vol. 73, No. 2. — journal of. August 2009 physics pp. 287–297. Classical and quantum mechanics of complex. Hamiltonian systems: An extended complex phase space ... 1Department of Physics, Ramjas College (University Enclave), University of Delhi,. Delhi 110 ... 1.1 Motivation behind the study of complex Hamiltonians.
Collapse and equilibrium of rotating, adiabatic clouds
International Nuclear Information System (INIS)
Boss, A.P.
1980-01-01
A numerical hydrodynamics computer code has been used to follow the collapse and establishment of equilibrium of adiabatic gas clouds restricted to axial symmetry. The clouds are initially uniform in density and rotation, with adiabatic exponents γ=5/3 and 7/5. The numerical technique allows, for the first time, a direct comparison to be made between the dynamic collapse and approach to equilibrium of unconstrained clouds on the one hand, and the results for incompressible, uniformly rotating equilibrium clouds, and the equilibrium structures of differentially rotating polytropes, on the other hand
The hamiltonian index of a graph and its branch-bonds
Xiong, Liming; Broersma, Haitze J.; Li, Xueliang; Li, Xueliang; Li, MingChu
2004-01-01
Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(G) is hamiltonian is called the hamiltonian index of G, denoted by h(G). A reduction method to determine the hamiltonian index of a graph G with h(G) ≤ 2 is given here. We
15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics
Passante, Roberto; Trapani, Camillo
2016-01-01
This book presents the Proceedings of the 15th International Conference on Non-Hermitian Hamiltonians in Quantum Physics, held in Palermo, Italy, from 18 to 23 May 2015. Non-Hermitian operators, and non-Hermitian Hamiltonians in particular, have recently received considerable attention from both the mathematics and physics communities. There has been a growing interest in non-Hermitian Hamiltonians in quantum physics since the discovery that PT-symmetric Hamiltonians can have a real spectrum and thus a physical relevance. The main subjects considered in this book include: PT-symmetry in quantum physics, PT-optics, Spectral singularities and spectral techniques, Indefinite-metric theories, Open quantum systems, Krein space methods, and Biorthogonal systems and applications. The book also provides a summary of recent advances in pseudo-Hermitian Hamiltonians and PT-symmetric Hamiltonians, as well as their applications in quantum physics and in the theory of open quantum systems.
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
International Nuclear Information System (INIS)
Bellucci, Stefano; Nersessian, Armen; Yeranyan, Armen
2006-01-01
We apply the technique of Hamiltonian reduction for the construction of three-dimensional N=4 supersymmetric mechanics specified by the presence of a Dirac monopole. For this purpose we take the conventional N=4 supersymmetric mechanics on the four-dimensional conformally-flat spaces and perform its Hamiltonian reduction to three-dimensional system. We formulate the final system in the canonical coordinates, and present, in these terms, the explicit expressions of the Hamiltonian and supercharges. We show that, besides a magnetic monopole field, the resulting system is specified by the presence of a spin-orbit coupling term. A comparision with previous work is also carried out
New Hamiltonian constraint operator for loop quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Yang, Jinsong, E-mail: yangksong@gmail.com [Department of Physics, Guizhou university, Guiyang 550025 (China); Institute of Physics, Academia Sinica, Taiwan (China); Ma, Yongge, E-mail: mayg@bnu.edu.cn [Department of Physics, Beijing Normal University, Beijing 100875 (China)
2015-12-17
A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
New Hamiltonian constraint operator for loop quantum gravity
Directory of Open Access Journals (Sweden)
Jinsong Yang
2015-12-01
Full Text Available A new symmetric Hamiltonian constraint operator is proposed for loop quantum gravity, which is well defined in the Hilbert space of diffeomorphism invariant states up to non-planar vertices with valence higher than three. It inherits the advantage of the original regularization method to create new vertices to the spin networks. The quantum algebra of this Hamiltonian is anomaly-free on shell, and there is less ambiguity in its construction in comparison with the original method. The regularization procedure for this Hamiltonian constraint operator can also be applied to the symmetric model of loop quantum cosmology, which leads to a new quantum dynamics of the cosmological model.
The Hamiltonian structure of general relativistic perfect fluids
International Nuclear Information System (INIS)
Bao, D.; Houston Univ., TX; Marsden, J.; Walton, R.
1985-01-01
We show that the evolution equations for a perfect fluid coupled to general relativity in a general lapse and shift, are Hamiltonian relative to a certain Poisson structure. For the fluid variables, a Lie-Poisson structure associated to the dual of a semi-direct product Lie algebra is used, while the bracket for the gravitational variables has the usual canonical symplectic structure. The evolution is governed by a Hamiltonian which is equivalent to that obtained from a canonical analysis. The relationship of our Hamiltonian structure with other approaches in the literature, such as Clebsch potentials, Lagrangian to Eulerian transformations, and its use in clarifying linearization stability, are discussed. (orig.)
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
Energy Technology Data Exchange (ETDEWEB)
Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B. [Research Department of Biomedical Engineering, Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190 (China); Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn [School of Science, Harbin Institute of Technology, Shenzhen 518055 (China)
2017-08-20
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
International Nuclear Information System (INIS)
Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B.; Qin, G.
2017-01-01
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
Calculation of a hydrogen molecule in the adiabatic approximation
International Nuclear Information System (INIS)
Vukajlovich, F.R.; Mogilevskij, O.A.; Ponomarev, L.I.
1979-01-01
The adiabatic approximation js used for calculating the energy levels of a hydrogen molecule, i.e. of the simplest four-body system with a Coulomb interaction. The aim of this paper is the investigation of the possible use of the adiabatic method in the molecular problems. The most effective regions of its application are discussed. An infinite system of integro-differential equations is constructed, which describes the hydrogen molecule in the adiabatic approximation with the effective potentials taking into account the corrections to the nuclear motion. The energy of the first three vibrational states of the hydrogen molecule is calculated and compared with the experimental data. The convergence of the method is discussed
An effective Hamiltonian approach to quantum random walk
Indian Academy of Sciences (India)
2017-02-09
Feb 9, 2017 ... Abstract. In this article we present an effective Hamiltonian approach for discrete time quantum random walk. A form of the Hamiltonian for one-dimensional quantum walk has been prescribed, utilizing the fact that Hamil- tonians are generators of time translations. Then an attempt has been made to ...
International Nuclear Information System (INIS)
Proville, L.
1998-01-01
This thesis brings its contribution to the bipolaronic theory which might explain the origin of superconductivity at high temperature. A polaron is a quasiparticle made up of a localized electron and a deformation in the crystal structure. 2 electrons in singlet states localized on the same site form a bipolaron. Whenever the Coulomb repulsion between the 2 electrons is too strong bipolaron turns into 2 no bound polarons. We study the existence and the mobility of bipolarons. We describe the electron-phonon interaction by the Holstein term and the Coulomb repulsion by the Hubbard term. 2 assumptions are made: - the local electron-phonon interaction is strong and opposes the Coulomb repulsion between Hubbard type electrons - the system is close to the adiabatic limit. The system is reduced to 2 electrons in order to allow an exact treatment and the investigation of some bipolaronic bound states. At 2-dimensions the existence of bipolarons requires a very strong coupling which forbids any classical mobility. In some cases an important tunneling effect appears and we show that mobile bipolarons exist in a particular parameter range. Near the adiabatic limit we prove that polaronic and bipolaronic structures exist for a great number of electrons. (A.C.)
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)
Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.
Yang, Yongliang; Wunsch, Donald; Yin, Yixin
2017-08-01
This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.
On infinite walls in deformation quantization
International Nuclear Information System (INIS)
Kryukov, S.; Walton, M.A.
2005-01-01
We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In deformation quantization, considered as an autonomous formulation of quantum mechanics, the Wigner function of stationary states must be found by solving the so-called *-genvalue ('stargenvalue') equation for the Hamiltonian. For the cases considered here, this pseudo-differential equation is difficult to solve directly, without an ad hoc modification of the potential. Here we treat the infinite wall as the limit of a solvable exponential potential. Before the limit is taken, the corresponding *-genvalue equation involves the Wigner function at momenta translated by imaginary amounts. We show that it can be converted to a partial differential equation, however, with a well-defined limit. We demonstrate that the Wigner functions calculated from the standard Schroedinger wave functions satisfy the resulting new equation. Finally, we show how our results may be adapted to allow for the presence of another, non-singular part in the potential
Energy Technology Data Exchange (ETDEWEB)
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M., E-mail: champ@neu.edu [Department of Physics and Center for Interdisciplinary Research on Complex Systems,Northeastern University, Boston, Massachusetts 02115 (United States)
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical “gating” distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working
Introduction to thermodynamics of spin models in the Hamiltonian limit
Energy Technology Data Exchange (ETDEWEB)
Berche, Bertrand [Groupe M, Laboratoire de Physique des Materiaux, UMR CNRS No 7556, Universite Henri Poincare, Nancy 1, BP 239, F-54506 Vandoeuvre les Nancy, (France); Lopez, Alexander [Instituto Venezolano de Investigaciones CientIficas, Centro de Fisica, Carr. Panamericana, km 11, Altos de Pipe, Aptdo 21827, 1020-A Caracas, (Venezuela)
2006-01-01
A didactic description of the thermodynamic properties of classical spin systems is given in terms of their quantum counterpart in the Hamiltonian limit. Emphasis is on the construction of the relevant Hamiltonian and the calculation of thermal averages is explicitly done in the case of small systems described, in Hamiltonian field theory, by small matrices. The targeted students are those of a graduate statistical physics course.
Narrow-line laser cooling by adiabatic transfer
Norcia, Matthew A.; Cline, Julia R. K.; Bartolotta, John P.; Holland, Murray J.; Thompson, James K.
2018-02-01
We propose and demonstrate a novel laser cooling mechanism applicable to particles with narrow-linewidth optical transitions. By sweeping the frequency of counter-propagating laser beams in a sawtooth manner, we cause adiabatic transfer back and forth between the ground state and a long-lived optically excited state. The time-ordering of these adiabatic transfers is determined by Doppler shifts, which ensures that the associated photon recoils are in the opposite direction to the particle’s motion. This ultimately leads to a robust cooling mechanism capable of exerting large forces via a weak transition and with reduced reliance on spontaneous emission. We present a simple intuitive model for the resulting frictional force, and directly demonstrate its efficacy for increasing the total phase-space density of an atomic ensemble. We rely on both simulation and experimental studies using the 7.5 kHz linewidth 1S0 to 3P1 transition in 88Sr. The reduced reliance on spontaneous emission may allow this adiabatic sweep method to be a useful tool for cooling particles that lack closed cycling transitions, such as molecules.
Hamiltonian dynamics of preferential attachment
International Nuclear Information System (INIS)
Zuev, Konstantin; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2016-01-01
Prediction and control of network dynamics are grand-challenge problems in network science. The lack of understanding of fundamental laws driving the dynamics of networks is among the reasons why many practical problems of great significance remain unsolved for decades. Here we study the dynamics of networks evolving according to preferential attachment (PA), known to approximate well the large-scale growth dynamics of a variety of real networks. We show that this dynamics is Hamiltonian, thus casting the study of complex networks dynamics to the powerful canonical formalism, in which the time evolution of a dynamical system is described by Hamilton’s equations. We derive the explicit form of the Hamiltonian that governs network growth in PA. This Hamiltonian turns out to be nearly identical to graph energy in the configuration model, which shows that the ensemble of random graphs generated by PA is nearly identical to the ensemble of random graphs with scale-free degree distributions. In other words, PA generates nothing but random graphs with power-law degree distribution. The extension of the developed canonical formalism for network analysis to richer geometric network models with non-degenerate groups of symmetries may eventually lead to a system of equations describing network dynamics at small scales. (paper)
Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories
Wang, Tenghui; Zhang, Zhenxing; Xiang, Liang; Gong, Zhihao; Wu, Jianlan; Yin, Yi
2018-04-01
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the "shortcut to adiabaticity" (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.
Landahl, Andrew
2012-10-01
Quantum computers promise to exploit counterintuitive quantum physics principles like superposition, entanglement, and uncertainty to solve problems using fundamentally fewer steps than any conventional computer ever could. The mere possibility of such a device has sharpened our understanding of quantum coherent information, just as lasers did for our understanding of coherent light. The chief obstacle to developing quantum computer technology is decoherence--one of the fastest phenomena in all of physics. In principle, decoherence can be overcome by using clever entangled redundancies in a process called fault-tolerant quantum error correction. However, the quality and scale of technology required to realize this solution appears distant. An exciting alternative is a proposal called ``adiabatic'' quantum computing (AQC), in which adiabatic quantum physics keeps the computer in its lowest-energy configuration throughout its operation, rendering it immune to many decoherence sources. The Adiabatic Quantum Architectures In Ultracold Systems (AQUARIUS) Grand Challenge Project at Sandia seeks to demonstrate this robustness in the laboratory and point a path forward for future hardware development. We are building devices in AQUARIUS that realize the AQC architecture on up to three quantum bits (``qubits'') in two platforms: Cs atoms laser-cooled to below 5 microkelvin and Si quantum dots cryo-cooled to below 100 millikelvin. We are also expanding theoretical frontiers by developing methods for scalable universal AQC in these platforms. We have successfully demonstrated operational qubits in both platforms and have even run modest one-qubit calculations using our Cs device. In the course of reaching our primary proof-of-principle demonstrations, we have developed multiple spinoff technologies including nanofabricated diffractive optical elements that define optical-tweezer trap arrays and atomic-scale Si lithography commensurate with placing individual donor atoms with
Hamiltonian formalisms and symmetries of the Pais–Uhlenbeck oscillator
Directory of Open Access Journals (Sweden)
Krzysztof Andrzejewski
2014-12-01
Full Text Available The study of the symmetry of Pais–Uhlenbeck oscillator initiated in Andrzejewski et al. (2014 [24] is continued with special emphasis put on the Hamiltonian formalism. The symmetry generators within the original Pais and Uhlenbeck Hamiltonian approach as well as the canonical transformation to the Ostrogradski Hamiltonian framework are derived. The resulting algebra of generators appears to be the central extension of the one obtained on the Lagrangian level; in particular, in the case of odd frequencies one obtains the centrally extended l-conformal Newton–Hooke algebra. In this important case the canonical transformation to an alternative Hamiltonian formalism (related to the free higher derivatives theory is constructed. It is shown that all generators can be expressed in terms of the ones for the free theory and the result agrees with that obtained by the orbit method.
Non-adiabatic generator-coordinate calculation of H2+
International Nuclear Information System (INIS)
Tostes, J.G.R.; Para Univ., Belem; Toledo Piza, A.F.R. de
1982-10-01
A non-adiabatic calculation of the few lowest J=O states in the H 2+ molecule done within the framework of the Generator Coordinate Method is reported. Substantial accuracy is achivied with the diagonalization of matrices of very modest dimensions. The resulting wavefunctions are strongly dominated by just a few basis states. The computational scheme is set up so as to take the best advantage of good analytical approximations to existing adiabatic molecular wavefunctions. (Author) [pt
Multivector field formulation of Hamiltonian field theories: equations and symmetries
Energy Technology Data Exchange (ETDEWEB)
Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N. [Departamento de Matematica Aplicada y Telematica, Edificio C-3, Campus Norte UPC, Barcelona (Spain)
1999-12-03
We state the intrinsic form of the Hamiltonian equations of first-order classical field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analysed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between Cartan-Noether symmetries and general symmetries of the system is discussed. Noether's theorem is also stated in this context, both the 'classical' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed. (author)
Variational derivation of a time-dependent Hartree-Fock Hamiltonian
International Nuclear Information System (INIS)
Lichtner, P.C.; Griffin, J.J.; Schultheis, H.; Schultheis, R.; Volkov, A.B.
1979-01-01
The variational derivation of the time-dependent Hartree-Fock equation is reviewed. When norm-violating variations are included, a unique time-dependent Hartree-Fock Hamiltonian, which differs from that customarily used in time-dependent Hartree-Fock analyses, is implied. This variationally ''true'' Hartree-Fock Hamiltonian has the same expectation value as the exact Hamiltonian, equal to the average energy of the system. Since this quantity remains constant under time-dependent Hartree-Fock time evolution, we suggest the label ''constant '' for this form of time-dependent Hartree-Fock theory
Toric codes and quantum doubles from two-body Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Brell, Courtney G; Bartlett, Stephen D; Doherty, Andrew C [Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney (Australia); Flammia, Steven T, E-mail: cbrell@physics.usyd.edu.au [Perimeter Institute for Theoretical Physics, Waterloo (Canada)
2011-05-15
We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Adiabatic supernova expansion into the circumstellar medium
International Nuclear Information System (INIS)
Band, D.L.; Liang, E.P.
1987-01-01
We perform one dimensional numerical simulations with a Lagrangian hydrodynamics code of the adiabatic expansion of a supernova into the surrounding medium. The early expansion follows Chevalier's analytic self-similar solution until the reverse shock reaches the ejecta core. We follow the expansion as it evolves towards the adiabatic blast wave phase. Some memory of the earlier phases of expansion is retained in the interior even when the outer regions expand as a blast wave. We find the results are sensitive to the initial configuration of the ejecta and to the placement of gridpoints. 6 refs., 2 figs
Dzyaloshinskii-Moriya interactions and adiabatic magnetization dynamics in molecular magnets
De Raedt, H; Miyashita, S; Michielsen, K; Machida, M
A microscopic model of the molecular magnet V-15 is used to study mechanisms for the adiabatic change of the magnetization in time-dependent magnetic fields. The effects of the Dzyaloshinskii-Moriya interaction, the most plausible source for the energy-level repulsions that lead to adiabatic changes
Port-Hamiltonian approaches to motion generation for mechanical systems
Sakai, Satoru; Stramigioli, Stefano
This paper gives new motion generation methods for mechanical port-Hamiltonian systems. First, we propose a generation method based on an asymptotic stabilization method without damping assignment. This asymptotic stabilization method preserves the Hamiltonian structure in the closed-loop system
The bi-Hamiltonian structures of the Manin-Radul super KP hierarchy
International Nuclear Information System (INIS)
Panda, S.; Roy, S.
1992-05-01
We consider the ''even-time'' flow of the Manin-Radul supersymmetric KP hierarchy and show that it possesses bi-Hamiltonian structures by deriving two distinct Gelfand-Dikii brackets corresponding to two successive Hamiltonians of the system. A recursion relation involving them is also obtained. We observe that the first Hamiltonian structure defines a supersymmetric Lie algebra since it is a linear algebra among the super fields appearing in the Lax operator whereas the second Hamiltonian structure is a non-linear algebra and so it does not define a Lie algebra. (author). 25 refs
Hamiltonian description of the ideal fluid
International Nuclear Information System (INIS)
Morrison, P.J.
1998-01-01
The Hamiltonian viewpoint of fluid mechanical systems with few and infinite number of degrees of freedom is described. Rudimentary concepts of finite-degree-of-freedom Hamiltonian dynamics are reviewed, in the context of the passive advection of a scalar or tracer field by a fluid. The notions of integrability, invariant-tori, chaos, overlap criteria, and invariant-tori breakup are described in this context. Preparatory to the introduction of field theories, systems with an infinite number of degrees of freedom, elements of functional calculus and action principles of mechanics are reviewed. The action principle for the ideal compressible fluid is described in terms of Lagrangian or material variables. Hamiltonian systems in terms of noncanonical variables are presented, including several examples of Eulerian or inviscid fluid dynamics. Lie group theory sufficient for the treatment of reduction is reviewed. The reduction from Lagrangian to Eulerian variables is treated along with Clebsch variable decompositions. Stability in the canonical and noncanonical Hamiltonian contexts is described. Sufficient conditions for stability, such as Rayleigh-like criteria, are seen to be only sufficient in the general case because of the existence of negative-energy modes, which are possessed by interesting fluid equilibria. Linearly stable equilibria with negative energy modes are argued to be unstable when nonlinearity or dissipation is added. The energy-Casimir method is discussed and a variant of it that depends upon the notion of dynamical accessibility is described. The energy content of a perturbation about a general fluid equilibrium is calculated using three methods. copyright 1998 The American Physical Society
Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
Bridges, Thomas J.; Reich, Sebastian
2001-06-01
The symplectic numerical integration of finite-dimensional Hamiltonian systems is a well established subject and has led to a deeper understanding of existing methods as well as to the development of new very efficient and accurate schemes, e.g., for rigid body, constrained, and molecular dynamics. The numerical integration of infinite-dimensional Hamiltonian systems or Hamiltonian PDEs is much less explored. In this Letter, we suggest a new theoretical framework for generalizing symplectic numerical integrators for ODEs to Hamiltonian PDEs in R2: time plus one space dimension. The central idea is that symplecticity for Hamiltonian PDEs is directional: the symplectic structure of the PDE is decomposed into distinct components representing space and time independently. In this setting PDE integrators can be constructed by concatenating uni-directional ODE symplectic integrators. This suggests a natural definition of multi-symplectic integrator as a discretization that conserves a discrete version of the conservation of symplecticity for Hamiltonian PDEs. We show that this approach leads to a general framework for geometric numerical schemes for Hamiltonian PDEs, which have remarkable energy and momentum conservation properties. Generalizations, including development of higher-order methods, application to the Euler equations in fluid mechanics, application to perturbed systems, and extension to more than one space dimension are also discussed.
Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats
Directory of Open Access Journals (Sweden)
Ricardo T. Paéz-Hernández
2017-11-01
Full Text Available This paper presents an analysis of a Curzon and Alhborn thermal engine model where both internal irreversibilities and non-instantaneous adiabatic branches are considered, operating with maximum ecological function and maximum power output regimes. Its thermodynamic properties are shown, and an analysis of its local dynamic stability is performed. The results derived are compared throughout the work with the results obtained previously for a case in which the adiabatic branches were assumed as instantaneous. The results indicate a better performance for thermodynamic properties in the model with instantaneous adiabatic branches, whereas there is an improvement in robustness in the case where non-instantaneous adiabatic branches are considered.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
The self-trapping of anion excitons in alkali halides at elastic deformation
International Nuclear Information System (INIS)
Tulepbergenov, S.K.; Dzhumanov, S.; Spivak-Lavrov, I.F.; Shunkeev, K.Sh.
2001-01-01
The self-trapping of electronic excitations (EE) (excitons, holes and electrons) in alkali halides (AH), fluorides and oxides plays an important roles in luminescence and defect formation. Therein the specific features of self-trapping of EE in various materials are essentially different. In particular, the self-trapping of excitons in some AH (i.e. alkali iodides and bromides) occurs with overcoming of the potential barrier and in other AH (e.g. alkali fluorides and chlorides) such a barrier is absent. Here we develop the continuum theory of self-trapping of within the adiabatic approximation elastically stressed AH. In the continuum model of solids the functional of the total energy of are interacting exciton-phonon system in the deformed ionic crystal just as in the undeformed crystal depends on the dilation Δ(r) described by the deformation potential of acoustic phonon, the electrostatic potential φ[r) due to the lattice polarization at optical lattice vibrations and the wave function of exciton chosen for hydro statically and uniaxially stressed 3D crystals. The functionals of the total energy of the interfacing exciton-phonon system E{Δ(r),φ(r),ψ(r)} are minimized relative to Δ, φ and ψ for the cases of isotropic and anisotropic 3D crystals. As a result, we obtained the functionals depending on μ and determined their possible extremum. We have show that the linear deformations under the hydrostatic and uniaxial stress at 80 K lead to the decreasing of the self trapping barrier for exciton and to the increasing of the luminescence of self-trapped excitons (STE). While the nonlinear deformations under the such stress at 80 K lead to the increasing of the self-trapping barrier for excitons and to the decreasing at the STE luminescence in AH. At T=0 K the small hydrostatic and uniaxial pressures lead to the same effects. Further at hydrostatic and uniaxial compressions of AH the minimums of the adiabatic potentials of quasifree and STE are shifted to
Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions
Directory of Open Access Journals (Sweden)
Philipp eHauke
2015-04-01
Full Text Available Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.
Bäcklund transformations and Hamiltonian flows
International Nuclear Information System (INIS)
Zullo, Federico
2013-01-01
In this work we show that, under certain conditions, parametric Bäcklund transformations for a finite dimensional integrable system can be interpreted as solutions to the equations of motion defined by an associated non-autonomous Hamiltonian. The two systems share the same constants of motion. This observation leads to the identification of the Hamiltonian interpolating the iteration of the discrete map defined by the transformations, which indeed in numerical applications can be considered a linear combination of the integrals appearing in the spectral curve of the Lax matrix. An example with the periodic Toda lattice is given. (paper)
Hamiltonian dynamics for complex food webs
Kozlov, Vladimir; Vakulenko, Sergey; Wennergren, Uno
2016-03-01
We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.
Dirac-bracket aproach to nearly-geostrophic Hamiltonian balanced models
Vanneste, J.; Bokhove, Onno
2002-01-01
Dirac’s theory of constrained Hamiltonian systems is applied to derive the Poisson structure of a class of balanced models describing the slow dynamics of geophysical flows. Working with the Poisson structure, instead of the canonical Hamiltonian structure previously considered in this context,
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
Structure preserving port-Hamiltonian model reduction of electrical circuits
Polyuga, R.; Schaft, van der A.J.; Benner, P.; Hinze, M.; Maten, ter E.J.W.
2011-01-01
This paper discusses model reduction of electrical circuits based on a port-Hamiltonian representation. It is shown that by the use of the Kalman decomposition an uncontrollable and/or unobservable port-Hamiltonian system is reduced to a controllable/observable system that inherits the
Hamiltonian boundary term and quasilocal energy flux
International Nuclear Information System (INIS)
Chen, C.-M.; Nester, James M.; Tung, R.-S.
2005-01-01
The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasilocal values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasilocal energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasilocal energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasilocal expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant
A note on the geometric phase in adiabatic approximation
International Nuclear Information System (INIS)
Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
2005-01-01
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough
Generalized internal long wave equations: construction, hamiltonian structure and conservation laws
International Nuclear Information System (INIS)
Lebedev, D.R.
1982-01-01
Some aspects of the theory of the internal long-wave equations (ILW) are considered. A general class of the ILW type equations is constructed by means of the Zakharov-Shabat ''dressing'' method. Hamiltonian structure and infinite numbers of conservation laws are introduced. The considered equations are shown to be Hamiltonian in the so-called second Hamiltonian structu
Port Hamiltonian Formulation of Infinite Dimensional Systems I. Modeling
Macchelli, Alessandro; Schaft, Arjan J. van der; Melchiorri, Claudio
2004-01-01
In this paper, some new results concerning the modeling of distributed parameter systems in port Hamiltonian form are presented. The classical finite dimensional port Hamiltonian formulation of a dynamical system is generalized in order to cope with the distributed parameter and multi-variable case.
An Adiabatic Phase-Matching Accelerator
Energy Technology Data Exchange (ETDEWEB)
Lemery, Francois [DESY; Floettmann, Klaus [DESY; Piot, Philippe [Northern Illinois U.; Kaertner, Franz X. [Hamburg U.; Assmann, Ralph [DESY
2017-12-22
We present a general concept to accelerate non-relativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program {\\sc astra} and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100~MV/m. The numerical simulations indicate that a $\\sim 200$-keV electron beam can be accelerated to an energy of $\\sim10$~MeV over $\\sim 10$~cm. The novel scheme is also found to form electron beams with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.
Diabatic and adiabatic representations for atomic collision processes
International Nuclear Information System (INIS)
Delos, J.B.; Thorson, W.R.
1979-01-01
A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity-dependent couplings in slow collisions, including the effects of electron-translation factors (ETF's). We compare the couplings arising from atomic representations and atomic ETF's with those arising from molecular representations and ''switching function'' ETF's. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then show that an acceptable general definition of a diabatic representation is provided by the condition P+A=0, where P is the usual nonadiabatic coupling matrix and A represents corrections to it arising from electron translation factors (ETF's). Two distinct types of diabatic representation result, depending on the definition taken for A. States that undergo no deformation are called F diabatic; those that have no velocity-dependent couplings are called M diabatic. Finally, we discuss the properties of representations that are partially diabatic and partially adiabatic, and we give some rules for the construction of representations that should be nearly optimal for describing many types of collision processes
Alternative Hamiltonian representation for gravity
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2007-01-01
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity
Ostrogradski Hamiltonian approach for geodetic brane gravity
International Nuclear Information System (INIS)
Cordero, Ruben; Molgado, Alberto; Rojas, Efrain
2010-01-01
We present an alternative Hamiltonian description of a branelike universe immersed in a flat background spacetime. This model is named geodetic brane gravity. We set up the Regge-Teitelboim model to describe our Universe where such field theory is originally thought as a second order derivative theory. We refer to an Ostrogradski Hamiltonian formalism to prepare the system to its quantization. This approach comprize the manage of both first- and second-class constraints and the counting of degrees of freedom follows accordingly.
Model reduction of port-Hamiltonian systems as structured systems
Polyuga, R.V.; Schaft, van der A.J.
2010-01-01
The goal of this work is to demonstrate that a specific projection-based model reduction method, which provides an H2 error bound, turns out to be applicable to port-Hamiltonian systems, preserving the port-Hamiltonian structure for the reduced order model, and, as a consequence, passivity.
Adiabatic transfer of energy fluctuations between membranes inside an optical cavity
Garg, Devender; Chauhan, Anil K.; Biswas, Asoka
2017-08-01
A scheme is presented for the adiabatic transfer of average fluctuations in the phonon number between two membranes in an optical cavity. We show that by driving the cavity modes with external time-delayed pulses, one can obtain an effect analogous to stimulated Raman adiabatic passage in the atomic systems. The adiabatic transfer of fluctuations from one membrane to the other is attained through a "dark" mode, which is robust against decay of the mediating cavity mode. The results are supported with analytical and numerical calculations with experimentally feasible parameters.
Vilasi, Gaetano
2001-01-01
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems. As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity. As a m
Exact smooth classification of Hamiltonian vector fields on symplectic 2-manifolds
International Nuclear Information System (INIS)
Krouglikov, B.S.
1994-10-01
Complete exact classification of Hamiltonian systems with one degree of freedom and Morse Hamiltonian is carried out. As it is a main part of trajectory classification of integrable Hamiltonian systems with two degrees of freedom, the corresponding generalization is considered. The dual problem of classification of symplectic form together with Morse foliation is carried out as well. (author). 10 refs, 16 figs
Convergence of hyperspherical adiabatic expansion for helium-like systems
International Nuclear Information System (INIS)
Abrashkevich, A.G.; Abrashkevich, D.G.; Pojda, V.Yu.; Vinitskij, S.I.; Kaschiev, M.S.; Puzynin, I.V.
1988-01-01
The convergence of hyperspherical adiabatic expansion has been studied numerically. The spectral problems arising after separation of variables are solved by the finite-difference and finite element methods. The energies of the ground and some doubly excited staes of a hydrogen ion are calculated in the six-channel approximation within the 10 -4 a.u. accuracy. Obtained results demonstrate a rapid convergence of the hyperspherical adiabatic expansion. 14 refs.; 5 tabs
New Hamiltonian structure of the fractional C-KdV soliton equation hierarchy
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2008-01-01
A generalized Hamiltonian structure of the fractional soliton equation hierarchy is presented by using of differential forms and exterior derivatives of fractional orders. Example of the fractional Hamiltonian system of the C-KdV soliton equation hierarchy is constructed, which is a new Hamiltonian structure
Hamiltonian formalism for perfect fluids in general relativity
International Nuclear Information System (INIS)
Demaret, J.; Moncrief, V.
1980-01-01
Schutz's Hamiltonian theory of a relativistic perfect fluid, based on the velocity-potential version of classical perfect fluid hydrodynamics as formulated by Seliger and Whitham, is used to derive, in the framework of the Arnowitt, Deser, and Misner (ADM) method, a general partially reduced Hamiltonian for relativistic systems filled with a perfect fluid. The time coordinate is chosen, as in Lund's treatment of collapsing balls of dust, as minus the only velocity potential different from zero in the case of an irrotational and isentropic fluid. A ''semi-Dirac'' method can be applied to quantize astrophysical and cosmological models in the framework of this partially reduced formalism. If one chooses Taub's adapted comoving coordinate system, it is possible to derive a fully reduced ADM Hamiltonian, which is equal to minus the total baryon number of the fluid, generalizing a result previously obtained by Moncrief in the more particular framework of Taub's variational principle, valid for self-gravitating barotropic relativistic perfect fluids. An unconstrained Hamiltonian density is then explicitly derived for a fluid obeying the equation of state p=(gamma-1)rho (1 < or = γ < or = 2), which can adequately describe the phases of very high density attained in a catastrophic collapse or during the early stages of the Universe. This Hamiltonian density, shown to be equivalent to Moncrief's in the particular case of an isentropic fluid, can be simplified for fluid-filled class-A diagonal Bianchi-type cosmological models and appears as a suitable starting point for the study of the canonical quantization of these models
A Hamiltonian functional for the linearized Einstein vacuum field equations
International Nuclear Information System (INIS)
Rosas-RodrIguez, R
2005-01-01
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained
The detectability lemma and its applications to quantum Hamiltonian complexity
International Nuclear Information System (INIS)
Aharonov, Dorit; Arad, Itai; Vazirani, Umesh; Landau, Zeph
2011-01-01
Quantum Hamiltonian complexity, an emerging area at the intersection of condensed matter physics and quantum complexity theory, studies the properties of local Hamiltonians and their ground states. In this paper we focus on a seemingly specialized technical tool, the detectability lemma (DL), introduced in the context of the quantum PCP challenge (Aharonov et al 2009 arXiv:0811.3412), which is a major open question in quantum Hamiltonian complexity. We show that a reformulated version of the lemma is a versatile tool that can be used in place of the celebrated Lieb-Robinson (LR) bound to prove several important results in quantum Hamiltonian complexity. The resulting proofs are much simpler, more combinatorial and provide a plausible path toward tackling some fundamental open questions in Hamiltonian complexity. We provide an alternative simpler proof of the DL that removes a key restriction in the original statement (Aharonov et al 2009 arXiv:0811.3412), making it more suitable for the broader context of quantum Hamiltonian complexity. Specifically, we first use the DL to provide a one-page proof of Hastings' result that the correlations in the ground states of gapped Hamiltonians decay exponentially with distance (Hastings 2004 Phys. Rev. B 69 104431). We then apply the DL to derive a simpler and more intuitive proof of Hastings' seminal one-dimensional (1D) area law (Hastings 2007 J. Stat. Mech. (2007) P8024) (both these proofs are restricted to frustration-free systems). Proving the area law for two and higher dimensions is one of the most important open questions in the field of Hamiltonian complexity, and the combinatorial nature of the DL-based proof holds out hope for a possible generalization. Indeed, soon after the first publication of the methods presented here, they were applied to derive exponential improvements to Hastings' result (Arad et al 2011, Aharonov et al 2011) in the case of frustration-free 1D systems. Finally, we also provide a more general
Kinetic Theory Derivation of the Adiabatic Law for Ideal Gases.
Sobel, Michael I.
1980-01-01
Discusses how the adiabatic law for ideal gases can be derived from the assumption of a Maxwell-Boltzmann (or any other) distribution of velocities--in contrast to the usual derivations from thermodynamics alone, and the higher-order effect that leads to one-body viscosity. An elementary derivation of the adiabatic law is given. (Author/DS)
Effective Hamiltonian within the microscopic unitary nuclear model
International Nuclear Information System (INIS)
Filippov, G.F.; Blokhin, A.L.
1989-01-01
A technique of projecting the microscopic nuclear Hamiltonian on the SU(3)-group enveloping algebra is developed. The approach proposed is based on the effective Hamiltonian restored from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation. 40 refs
Hamilton-Jacobi theorems for regular reducible Hamiltonian systems on a cotangent bundle
Wang, Hong
2017-09-01
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of Abraham and Marsden (1978), such that we can prove two types of geometric Hamilton-Jacobi theorem for a Hamiltonian system on the cotangent bundle of a configuration manifold, by using the symplectic form and dynamical vector field. Then these results are generalized to the regular reducible Hamiltonian system with symmetry and momentum map, by using the reduced symplectic form and the reduced dynamical vector field. The Hamilton-Jacobi theorems are proved and two types of Hamilton-Jacobi equations, for the regular point reduced Hamiltonian system and the regular orbit reduced Hamiltonian system, are obtained. As an application of the theoretical results, the regular point reducible Hamiltonian system on a Lie group is considered, and two types of Lie-Poisson Hamilton-Jacobi equation for the regular point reduced system are given. In particular, the Type I and Type II of Lie-Poisson Hamilton-Jacobi equations for the regular point reduced rigid body and heavy top systems are shown, respectively.
Alternative Hamiltonian representation for gravity
Energy Technology Data Exchange (ETDEWEB)
Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)
2007-11-15
By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.
Predicting the effect of relaxation during frequency-selective adiabatic pulses
Pfaff, Annalise R.; McKee, Cailyn E.; Woelk, Klaus
2017-11-01
Adiabatic half and full passages are invaluable for achieving uniform, B1-insensitive excitation or inversion of macroscopic magnetization across a well-defined range of NMR frequencies. To accomplish narrow frequency ranges with adiabatic pulses (computer-calculated data with experimental results demonstrates that, in non-viscous, small-molecule fluids, it is possible to model magnetization and relaxation by considering standard T1 and T2 relaxation in the traditional rotating frame. The proposed model is aimed at performance optimizations of applications in which these pulses are employed. It differs from previous reports which focused on short high-power adiabatic pulses and relaxation that is governed by dipole-dipole interactions, cross polarization, or chemical exchange.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
International Nuclear Information System (INIS)
Habib, K. M. Masum; Ghosh, Avik W.; Sajjad, Redwan N.
2016-01-01
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.
Modified Dirac Hamiltonian for efficient quantum mechanical simulations of micron sized devices
Energy Technology Data Exchange (ETDEWEB)
Habib, K. M. Masum, E-mail: masum.habib@virginia.edu; Ghosh, Avik W. [Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904 (United States); Sajjad, Redwan N. [Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2016-03-14
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian provides a possible way to circumvent this problem. We show that the modified Hamiltonian with the additional term results in a very small Hamiltonian matrix when discretized on a real space square lattice. The resulting Hamiltonian matrix is considerably more efficient for numerical simulations without sacrificing on accuracy and is several orders of magnitude faster than the atomistic tight binding model. Using this Hamiltonian and the non-equilibrium Green's function formalism, we show several transport phenomena in graphene, such as magnetic focusing, chiral tunneling in the ballistic limit, and conductivity in the diffusive limit in micron sized graphene devices. The modified Hamiltonian can be used for any system with massless Dirac fermions such as Topological Insulators, opening up a simulation domain that is not readily accessible otherwise.
Topological color codes and two-body quantum lattice Hamiltonians
Kargarian, M.; Bombin, H.; Martin-Delgado, M. A.
2010-02-01
Topological color codes are among the stabilizer codes with remarkable properties from the quantum information perspective. In this paper, we construct a lattice, the so-called ruby lattice, with coordination number 4 governed by a two-body Hamiltonian. In a particular regime of coupling constants, in a strong coupling limit, degenerate perturbation theory implies that the low-energy spectrum of the model can be described by a many-body effective Hamiltonian, which encodes the color code as its ground state subspace. Ground state subspace corresponds to a vortex-free sector. The gauge symmetry Z2×Z2 of the color code could already be realized by identifying three distinct plaquette operators on the ruby lattice. All plaquette operators commute with each other and with the Hamiltonian being integrals of motion. Plaquettes are extended to closed strings or string-net structures. Non-contractible closed strings winding the space commute with Hamiltonian but not always with each other. This gives rise to exact topological degeneracy of the model. A connection to 2-colexes can be established via the coloring of the strings. We discuss it at the non-perturbative level. The particular structure of the two-body Hamiltonian provides a fruitful interpretation in terms of mapping onto bosons coupled to effective spins. We show that high-energy excitations of the model have fermionic statistics. They form three families of high-energy excitations each of one color. Furthermore, we show that they belong to a particular family of topological charges. The emergence of invisible charges is related to the string-net structure of the model. The emerging fermions are coupled to nontrivial gauge fields. We show that for particular 2-colexes, the fermions can see the background fluxes in the ground state. Also, we use the Jordan-Wigner transformation in order to test the integrability of the model via introducing Majorana fermions. The four-valent structure of the lattice prevents the
New classes of nonlinear vector coherent states of generalized spin-orbit Hamiltonians
International Nuclear Information System (INIS)
Geloun, Joseph Ben; Norbert Hounkonnou, Mahouton
2009-01-01
This paper deals with an extension of our previous work (Ben Geloun and Hounkonnou 2007 J. Phys. A: Math. Theor. 40 F817) by considering an alternative construction of canonical and deformed vector coherent states (VCSs) of the Gazeau-Klauder type associated with generalized spin-orbit Hamiltonians. We define an annihilation operator which takes into account the finite-dimensional space of states induced by the k-photon transition processes of the two-level atom interacting with the single-mode radiation field. The class of nonlinear VCSs (NVCSs) corresponding to the action of the annihilation operator is deduced and expressed in terms of generalized displacement operators. Various NVCSs including their 'dual' counterparts are also discussed. Also, by using the Hilbert space structure, a new family of NVCSs parametrized by unit vectors of the S 3 sphere has been identified without making use of the annihilation operator.
An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation.
Ilias, Miroslav; Saue, Trond
2007-02-14
The authors report the implementation of a simple one-step method for obtaining an infinite-order two-component (IOTC) relativistic Hamiltonian using matrix algebra. They apply the IOTC Hamiltonian to calculations of excitation and ionization energies as well as electric and magnetic properties of the radon atom. The results are compared to corresponding calculations using identical basis sets and based on the four-component Dirac-Coulomb Hamiltonian as well as Douglas-Kroll-Hess and zeroth-order regular approximation Hamiltonians, all implemented in the DIRAC program package, thus allowing a comprehensive comparison of relativistic Hamiltonians within the finite basis approximation.
A hierarchy of Liouville integrable discrete Hamiltonian equations
Energy Technology Data Exchange (ETDEWEB)
Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn
2008-05-12
Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.
Families of superintegrable Hamiltonians constructed from exceptional polynomials
International Nuclear Information System (INIS)
Post, Sarah; Tsujimoto, Satoshi; Vinet, Luc
2012-01-01
We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable. (paper)
SOLVING THE HAMILTONIAN CYCLE PROBLEM USING SYMBOLIC DETERMINANTS
Ejov, V.; Filar, J. A.; Lucas, S. K.; Nelson, J. L.
2006-01-01
In this note we show how the Hamiltonian Cycle problem can be reduced to solving a system of polynomial equations related to the adjacency matrix of a graph. This system of equations can be solved using the method of Gröbner bases, but we also show how a symbolic determinant related to the adjacency matrix can be used to directly decide whether a graph has a Hamiltonian cycle.
Hamiltonian derivation of a gyrofluid model for collisionless magnetic reconnection
International Nuclear Information System (INIS)
Tassi, E
2014-01-01
We consider a simple electromagnetic gyrokinetic model for collisionless plasmas and show that it possesses a Hamiltonian structure. Subsequently, from this model we derive a two-moment gyrofluid model by means of a procedure which guarantees that the resulting gyrofluid model is also Hamiltonian. The first step in the derivation consists of imposing a generic fluid closure in the Poisson bracket of the gyrokinetic model, after expressing such bracket in terms of the gyrofluid moments. The constraint of the Jacobi identity, which every Poisson bracket has to satisfy, selects then what closures can lead to a Hamiltonian gyrofluid system. For the case at hand, it turns out that the only closures (not involving integro/differential operators or an explicit dependence on the spatial coordinates) that lead to a valid Poisson bracket are those for which the second order parallel moment, independently for each species, is proportional to the zero order moment. In particular, if one chooses an isothermal closure based on the equilibrium temperatures and derives accordingly the Hamiltonian of the system from the Hamiltonian of the parent gyrokinetic model, one recovers a known Hamiltonian gyrofluid model for collisionless reconnection. The proposed procedure, in addition to yield a gyrofluid model which automatically conserves the total energy, provides also, through the resulting Poisson bracket, a way to derive further conservation laws of the gyrofluid model, associated with the so called Casimir invariants. We show that a relation exists between Casimir invariants of the gyrofluid model and those of the gyrokinetic parent model. The application of such Hamiltonian derivation procedure to this two-moment gyrofluid model is a first step toward its application to more realistic, higher-order fluid or gyrofluid models for tokamaks. It also extends to the electromagnetic gyrokinetic case, recent applications of the same procedure to Vlasov and drift- kinetic systems
Trapped Ion Quantum Computation by Adiabatic Passage
International Nuclear Information System (INIS)
Feng Xuni; Wu Chunfeng; Lai, C. H.; Oh, C. H.
2008-01-01
We propose a new universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.
ADIABATIC HEATING OF CONTRACTING TURBULENT FLUIDS
International Nuclear Information System (INIS)
Robertson, Brant; Goldreich, Peter
2012-01-01
Turbulence influences the behavior of many astrophysical systems, frequently by providing non-thermal pressure support through random bulk motions. Although turbulence is commonly studied in systems with constant volume and mean density, turbulent astrophysical gases often expand or contract under the influence of pressure or gravity. Here, we examine the behavior of turbulence in contracting volumes using idealized models of compressed gases. Employing numerical simulations and an analytical model, we identify a simple mechanism by which the turbulent motions of contracting gases 'adiabatically heat', experiencing an increase in their random bulk velocities until the largest eddies in the gas circulate over a Hubble time of the contraction. Adiabatic heating provides a mechanism for sustaining turbulence in gases where no large-scale driving exists. We describe this mechanism in detail and discuss some potential applications to turbulence in astrophysical settings.
Adiabatic perturbation theory in quantum dynamics
Teufel, Stefan
2003-01-01
Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit. A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.
Weak KAM for commuting Hamiltonians
International Nuclear Information System (INIS)
Zavidovique, M
2010-01-01
For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax–Oleinik semi-groups, a result of Barles and Tourin (2001 Indiana Univ. Math. J. 50 1523–44), using a direct geometrical method (Stoke's theorem). We also obtain a 'generalization' of a theorem of Maderna (2002 Bull. Soc. Math. France 130 493–506). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton–Jacobi equation) for G and for H are the same. As a corollary we obtain the equality of the Aubry sets and of the Peierls barrier. This is also related to works of Sorrentino (2009 On the Integrability of Tonelli Hamiltonians Preprint) and Bernard (2007 Duke Math. J. 136 401–20)
Compact beam splitters in coupled waveguides using shortcuts to adiabaticity
Chen, Xi; Wen, Rui-Dan; Shi, Jie-Long; Tseng, Shuo-Yen
2018-04-01
There are various works on adiabatic (three) waveguide coupler devices but most are focused on the quantum optical analogies and the physics itself. We successfully apply shortcuts to adiabaticity techniques to the coupled waveguide system with a suitable length for integrated optics devices. Especially, the counter-diabatic driving protocol followed by unitary transformation overcomes the previously unrealistic implemention, and is used to design feasible and robust 1 × 2 and 1 × 3 beam splitters for symmetric and asymmetric three waveguide couplers. Numerical simulations with the beam propagation method demonstrate that these shortcut designs for beam splitters are shorter than the adiabatic ones, and also have a better tolerance than parallel waveguides resonant beam splitters with respect to spacing errors and wavelength variation.
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Hamiltonian mechanics and divergence-free fields
International Nuclear Information System (INIS)
Boozer, A.H.
1986-08-01
The field lines, or integral curves, of a divergence-free field in three dimensions are shown to be topologically equivalent to the trajectories of a Hamiltonian with two degrees of freedom. The consideration of fields that depend on a parameter allow the construction of a canonical perturbation theory which is valid even if the perturbation is large. If the parametric dependence of the magnetic, or the vorticity field is interpreted as time dependence, evolution equations are obtained which give Kelvin's theorem or the flux conservation theorem for ideal fluids and plasmas. The Hamiltonian methods prove especially useful for study of fields in which the field lines must be known throughout a volume of space
Adiabatic Expansion of Electron Gas in a Magnetic Nozzle
Takahashi, Kazunori; Charles, Christine; Boswell, Rod; Ando, Akira
2018-01-01
A specially constructed experiment shows the near perfect adiabatic expansion of an ideal electron gas resulting in a polytropic index greater than 1.4, approaching the adiabatic value of 5 /3 , when removing electric fields from the system, while the polytropic index close to unity is observed when the electrons are trapped by the electric fields. The measurements were made on collisionless electrons in an argon plasma expanding in a magnetic nozzle. The collision lengths of all electron collision processes are greater than the scale length of the expansion, meaning the system cannot be in thermodynamic equilibrium, yet thermodynamic concepts can be used, with caution, in explaining the results. In particular, a Lorentz force, created by inhomogeneities in the radial plasma density, does work on the expanding magnetic field, reducing the internal energy of the electron gas that behaves as an adiabatically expanding ideal gas.
Construction of alternative Hamiltonian structures for field equations
Energy Technology Data Exchange (ETDEWEB)
Herrera, Mauricio [Departamento de Fisica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Santiago (Chile); Hojman, Sergio A. [Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago (Chile); Facultad de Educacion, Universidad Nacional Andres Bello, Santiago (Chile); Centro de Recursos Educativos Avanzados, CREA, Santiago (Chile)
2001-08-10
We use symmetry vectors of nonlinear field equations to build alternative Hamiltonian structures. We construct such structures even for equations which are usually believed to be non-Hamiltonian such as heat, Burger and potential Burger equations. We improve on a previous version of the approach using recursion operators to increase the rank of the Poisson bracket matrices. Cole-Hopf and Miura-type transformations allow the mapping of these structures from one equation to another. (author)
Maslov index for Hamiltonian systems
Directory of Open Access Journals (Sweden)
Alessandro Portaluri
2008-01-01
Full Text Available The aim of this article is to give an explicit formula for computing the Maslov index of the fundamental solutions of linear autonomous Hamiltonian systems in terms of the Conley-Zehnder index and the map time one flow.
An extended discrete gradient formula for oscillatory Hamiltonian systems
International Nuclear Information System (INIS)
Liu Kai; Shi Wei; Wu Xinyuan
2013-01-01
In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)
A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy
International Nuclear Information System (INIS)
Wu, Guo-cheng; Zhang, Sheng
2011-01-01
In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus. -- Highlights: → A generalized Tu formula is first established based on the fractional variational theory for non-differentiable functions. → Hamiltonian structures of fractional AKNS hierarchy are obtained. → The classical AKNS hierarchy is just a special case of the fractional hierarchy.
A generalized Tu formula and Hamiltonian structures of fractional AKNS hierarchy
Energy Technology Data Exchange (ETDEWEB)
Wu, Guo-cheng, E-mail: wuguocheng2002@yahoo.com.cn [Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, Sichuan 641112 (China); College of Mathematics and Information Science, Neijiang Normal University, Neijiang, Sichuan 641112 (China); Zhang, Sheng, E-mail: zhshaeng@yahoo.com.cn [School of Mathematical Sciences, Dalian University of Technology, Dalian 116024 (China)
2011-10-03
In this Letter, a generalized Tu formula is firstly presented to construct Hamiltonian structures of fractional soliton equations. The obtained results can be reduced to the classical Hamiltonian hierarchy of AKNS in ordinary calculus. -- Highlights: → A generalized Tu formula is first established based on the fractional variational theory for non-differentiable functions. → Hamiltonian structures of fractional AKNS hierarchy are obtained. → The classical AKNS hierarchy is just a special case of the fractional hierarchy.
Formulation of Hamiltonian mechanics with even and odd Poisson brackets
International Nuclear Information System (INIS)
Khudaverdyan, O.M.; Nersesyan, A.P.
1987-01-01
A possibility is studied as to constrict the odd Poisson bracket and odd Hamiltonian by the given dynamics in phase superspace - the even Poisson bracket and even Hamiltonian so the transition to the new structure does not change the equations of motion. 9 refs
Simulation of adiabatic thermal beams in a periodic solenoidal magnetic focusing field
Directory of Open Access Journals (Sweden)
T. J. Barton
2012-12-01
Full Text Available Self-consistent particle-in-cell simulations are performed to verify earlier theoretical predictions of adiabatic thermal beams in a periodic solenoidal magnetic focusing field [K. R. Samokhvalova, J. Zhou, and C. Chen, Phys. Plasmas 14, 103102 (2007PHPAEN1070-664X10.1063/1.2779281; J. Zhou, K. R. Samokhvalova, and C. Chen, Phys. Plasmas 15, 023102 (2008PHPAEN1070-664X10.1063/1.2837891]. In particular, results are obtained for adiabatic thermal beams that do not rotate in the Larmor frame. For such beams, the theoretical predictions of the rms beam envelope, the conservations of the rms thermal emittances, the adiabatic equation of state, and the Debye length are verified in the simulations. Furthermore, the adiabatic thermal beam is found be stable in the parameter regime where the simulations are performed.
Orbits and variational principles for conservative Hamiltonian systems
International Nuclear Information System (INIS)
Torres del Castillo, G.F.
1989-01-01
It is shown that for any Hamiltonian system whose Hamiltonian is time-independent the equations that determine the orbits followed by the system, without making reference to time, have the form of Hamilton's equations in a phase space of dimension two units smaller than that of the original phase space. By considering the cases of classical mechanics and of geometrical optics, it is shown that this result amounts, respectively, to Maupertuis' least action principle and to Fermat's principle. (Author)
Cluster expansion for ground states of local Hamiltonians
Directory of Open Access Journals (Sweden)
Alvise Bastianello
2016-08-01
Full Text Available A central problem in many-body quantum physics is the determination of the ground state of a thermodynamically large physical system. We construct a cluster expansion for ground states of local Hamiltonians, which naturally incorporates physical requirements inherited by locality as conditions on its cluster amplitudes. Applying a diagrammatic technique we derive the relation of these amplitudes to thermodynamic quantities and local observables. Moreover we derive a set of functional equations that determine the cluster amplitudes for a general Hamiltonian, verify the consistency with perturbation theory and discuss non-perturbative approaches. Lastly we verify the persistence of locality features of the cluster expansion under unitary evolution with a local Hamiltonian and provide applications to out-of-equilibrium problems: a simplified proof of equilibration to the GGE and a cumulant expansion for the statistics of work, for an interacting-to-free quantum quench.
Convergence to equilibrium under a random Hamiltonian
Brandão, Fernando G. S. L.; Ćwikliński, Piotr; Horodecki, Michał; Horodecki, Paweł; Korbicz, Jarosław K.; Mozrzymas, Marek
2012-09-01
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Continuum-time Hamiltonian for the Baxter's model
International Nuclear Information System (INIS)
Libero, V.L.
1983-01-01
The associated Hamiltonian for the symmetric eight-vertex model is obtained by taking the time-continuous limit in an equivalent Ashkin-Teller model. The result is a Heisenberg Hamiltonian with coefficients J sub(x), J sub(y) and J sub(z) identical to those found by Sutherland for choices of the parameters a, b, c and d that bring the model close to the transition. The change in the operators is accomplished explicitly, the relation between the crossover operator for the Ashkin-Teller model and the energy operator for the eight-vertex model being obtained in a transparent form. (Author) [pt
Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy
International Nuclear Information System (INIS)
Zhang, Yufeng; Fan, Engui
2006-01-01
A scheme for deducing Hamiltonian structures of the higher-dimensional hierarchies of evolution equations is presented which is devoting to obtaining the Hamiltonian structures of integrable coupling of the Jaulent-Miodek hierarchy
Image-based visual servo control using the port-Hamiltonian Approach
Muñoz Arias, Mauricio; El Hawwary, Mohamed; Scherpen, Jacquelien M.A.
2015-01-01
This work is devoted to an image-based visual servo control strategy for standard mechanical systems in the port-Hamiltonian framework. We utilize a change of variables that transforms the port-Hamiltonian system into one with constant mass-inertia matrix, and we use an interaction matrix that
Phase transitions in the Hubbard Hamiltonian
International Nuclear Information System (INIS)
Chaves, C.M.; Lederer, P.; Gomes, A.A.
1977-05-01
Phase transition in the isotropic non-degenerate Hubbard Hamiltonian within the renormalization group techniques is studied, using the epsilon = 4 - d expansion to first order in epsilon. The functional obtained from the Hubbard Hamiltonian displays full rotation symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences on the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalization of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed
Hamiltonian partial differential equations and applications
Nicholls, David; Sulem, Catherine
2015-01-01
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Resolving the issue of branched Hamiltonian in modified Lanczos-Lovelock gravity
Ruz, Soumendranath; Mandal, Ranajit; Debnath, Subhra; Sanyal, Abhik Kumar
2016-07-01
The Hamiltonian constraint H_c = N{H} = 0, defines a diffeomorphic structure on spatial manifolds by the lapse function N in general theory of relativity. However, it is not manifest in Lanczos-Lovelock gravity, since the expression for velocity in terms of the momentum is multivalued. Thus the Hamiltonian is a branch function of momentum. Here we propose an extended theory of Lanczos-Lovelock gravity to construct a unique Hamiltonian in its minisuperspace version, which results in manifest diffeomorphic invariance and canonical quantization.
Adiabatic analysis of collisions. III. Remarks on the spin model
International Nuclear Information System (INIS)
Fano, U.
1979-01-01
Analysis of a spin-rotation model illustrates how transitions between adiabatic channel states stem from the second, rather than from the first, rate of change of these states, provided that appropriate identification of channels and scaling of the independent variable are used. These remarks, like the earlier development of a post-adiabatic approach, aim at elucidating the surprising success of approximate separation of variables in the treatment of complex mechanical systems
Non-Adiabatic Molecular Dynamics Methods for Materials Discovery
Energy Technology Data Exchange (ETDEWEB)
Furche, Filipp [Univ. of California, Irvine, CA (United States); Parker, Shane M. [Univ. of California, Irvine, CA (United States); Muuronen, Mikko J. [Univ. of California, Irvine, CA (United States); Roy, Saswata [Univ. of California, Irvine, CA (United States)
2017-04-04
The flow of radiative energy in light-driven materials such as photosensitizer dyes or photocatalysts is governed by non-adiabatic transitions between electronic states and cannot be described within the Born-Oppenheimer approximation commonly used in electronic structure theory. The non-adiabatic molecular dynamics (NAMD) methods based on Tully surface hopping and time-dependent density functional theory developed in this project have greatly extended the range of molecular materials that can be tackled by NAMD simulations. New algorithms to compute molecular excited state and response properties efficiently were developed. Fundamental limitations of common non-linear response methods were discovered and characterized. Methods for accurate computations of vibronic spectra of materials such as black absorbers were developed and applied. It was shown that open-shell TDDFT methods capture bond breaking in NAMD simulations, a longstanding challenge for single-reference molecular dynamics simulations. The methods developed in this project were applied to study the photodissociation of acetaldehyde and revealed that non-adiabatic effects are experimentally observable in fragment kinetic energy distributions. Finally, the project enabled the first detailed NAMD simulations of photocatalytic water oxidation by titania nanoclusters, uncovering the mechanism of this fundamentally important reaction for fuel generation and storage.
Time and a physical Hamiltonian for quantum gravity.
Husain, Viqar; Pawłowski, Tomasz
2012-04-06
We present a nonperturbative quantization of general relativity coupled to dust and other matter fields. The dust provides a natural time variable, leading to a physical Hamiltonian with spatial diffeomorphism symmetry. The surprising feature is that the Hamiltonian is not a square root. This property, together with the kinematical structure of loop quantum gravity, provides a complete theory of quantum gravity, and puts applications to cosmology, quantum gravitational collapse, and Hawking radiation within technical reach. © 2012 American Physical Society
On the topological entropy of an optical Hamiltonian flow
Niche, Cesar J.
2000-01-01
In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of the flow, restricted to the Lagrangian distribution or to a proper modification.
International Nuclear Information System (INIS)
Myung, Yun Soo
2010-01-01
We study graviton propagations of scalar, vector, and tensor modes in the deformed Horava-Lifshitz gravity (λR-model) without projectability condition. The quadratic Lagrangian is invariant under diffeomorphism only for λ=1 case, which contradicts to the fact that λ is irrelevant to a consistent Hamiltonian approach to the λR-model. In this case, as far as scalar propagations are concerned, there is no essential difference between deformed Horava-Lifshitz gravity (λR-model) and general relativity. This implies that there are two degrees of freedom for a massless graviton without Horava scalar, and five degrees of freedom appear for a massive graviton when introducing Lorentz-violating and Fierz-Pauli mass terms. Finally, it is shown that for λ=1, the vDVZ discontinuity is absent in the massless limit of Lorentz-violating mass terms by considering external source terms.
Adiabatic flame temperature of sodium combustion and sodium-water reaction
International Nuclear Information System (INIS)
Okano, Y.; Yamaguchi, A.
2001-01-01
In this paper, background information of sodium fire and sodium-water reaction accidents of LMFBR (liquid metal fast breeder reactor) is mentioned at first. Next, numerical analysis method of GENESYS is described in detail. Next, adiabatic flame temperature and composition of sodium combustion are analyzed, and affect of reactant composition, such oxygen and moisture, is discussed. Finally, adiabatic reaction zone temperature and composition of sodium-water reaction are calculated, and affects of reactant composition, sodium vaporization, and pressure are stated. Chemical equilibrium calculation program for generic chemical system (GENESYS) is developed in this study for the research on adiabatic flame temperature of sodium combustion and adiabatic reaction zone temperature of sodium-water reaction. The maximum flame temperature of the sodium combustion is 1,950 K at the standard atmospheric condition, and is not affected by the existence of moisture. The main reaction product is Na 2 O (l) , and in combustion in moist air, with NaOH (g) . The maximum reaction zone temperature of the sodium-water reaction is 1,600 K, and increases with the system pressure. The main products are NaOH (g) , NaOH (l) and H2 (g) . Sodium evaporation should be considered in the cases of sodium-rich and high pressure above 10 bar
Effective Hamiltonian for protected edge states in graphene
International Nuclear Information System (INIS)
Winkler, R.; Deshpande, H.
2017-01-01
Edge states in topological insulators (TIs) disperse symmetrically about one of the time-reversal invariant momenta Λ in the Brillouin zone (BZ) with protected degeneracies at Λ. Commonly TIs are distinguished from trivial insulators by the values of one or multiple topological invariants that require an analysis of the bulk band structure across the BZ. We propose an effective two-band Hamiltonian for the electronic states in graphene based on a Taylor expansion of the tight-binding Hamiltonian about the time-reversal invariant M point at the edge of the BZ. This Hamiltonian provides a faithful description of the protected edge states for both zigzag and armchair ribbons, though the concept of a BZ is not part of such an effective model. In conclusion, we show that the edge states are determined by a band inversion in both reciprocal and real space, which allows one to select Λ for the edge states without affecting the bulk spectrum.
Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems
International Nuclear Information System (INIS)
Prieto-Martinez, Pedro Daniel; Roman-Roy, Narciso
2011-01-01
The Lagrangian-Hamiltonian unified formalism of Skinner and Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher order field theories. However, a complete generalization to higher order mechanical systems is yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view. (paper)
Effective Hamiltonian theory: recent formal results and non-nuclear applications
International Nuclear Information System (INIS)
Brandow, B.H.
1981-01-01
Effective Hamiltonian theory is discussed from the points of view of the unitary transformation method and degenerate perturbation theory. It is shown that the two approaches are identical term by term. The main features of a formulation of the coupled-cluster method for open-shell systems are outlined. Finally, recent applications of the many-body linked-cluster form of degenerate perturbation theory are described: the derivation of effective spin Hamiltonians in magnetic insulator systems, the derivation and calculation ab initio of effective π-electron Hamiltonians for planar conjugated hydrocarbon molecules, and understanding the so-called valence fluctuation phenomenon exhibited by certain rare earth compounds
The q-deformed SU(2) Heisenberg model in 3-dimensions
International Nuclear Information System (INIS)
Lu Zhongyi; Yan Hong.
1991-07-01
A q-deformed SU(2) Heisenberg (3-dimensional) spin model is set up, and the q-deformed spin-wave solution is obtained through the q-analogous Holstein-Primakoff transformation. The result is given for small γ = ln q, which is the quantity characterizing the nonlinearity of the Hamiltonian. A mean-field treatment is arranged to preserved (at least some of) the nonlinearity, and the ordinary ferromagnet ground state is shown as the exact ground state of the new system. Interesting results are obtained for this nonlinear model: (i) There is an energy gap between the ground state and the first excited one, thus the ground state is stable under small perturbation of the background; (ii) the specific heat per volume is modified by a small term proportional to the 1/2-th power of temperature and the square of γ, which is qualitatively different from the conventional model, and (iii) the magnetization M(T) is modified by a factor that depends on γ. (author). 16 refs
Hamiltonian description of bubble dynamics
International Nuclear Information System (INIS)
Maksimov, A. O.
2008-01-01
The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.
A Hamiltonian approach to Thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)
2016-10-15
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
A Hamiltonian approach to Thermodynamics
International Nuclear Information System (INIS)
Baldiotti, M.C.; Fresneda, R.; Molina, C.
2016-01-01
In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.
Chou, Chia-Chun; Kouri, Donald J
2013-04-25
We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.
Adiabatic invariance with first integrals of motion
Adib, Artur B.
2002-10-01
The construction of a microthermodynamic formalism for isolated systems based on the concept of adiabatic invariance is an old but seldom appreciated effort in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33, 225 (1910)]. An apparently independent extension of such formalism for systems bearing additional first integrals of motion was recently proposed by Hans H. Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic invariance even in such singular cases. After some remarks in connection with the formalism pioneered by Hertz, it will be suggested that such an extension can incidentally explain the success of a dynamical method for computing the entropy of classical interacting fluids, at least in some potential applications where the presence of additional first integrals cannot be ignored.
Adiabatic compression of elongated field-reversed configurations
Energy Technology Data Exchange (ETDEWEB)
Spencer, R.L.; Tuszewski, M.; Linford, R.K.
1982-01-01
The simplest model of plasma dynamics is the adiabatic model. In this model the plasma is assumed to be in MHD equilibrium at each instant of time. The equilibria are connected by the requirement that they all have the same entropy per unit flux, i.e., the equilibria form a sequence generated by adiabatic changes. The standard way of computing such a sequence of equilibria was developed by Grad, but its practical use requires a fairly complicated code. It would be helpful if approximately the same results could be gotten either with a much simpler code or by analytical techniques. In Sec. II a one-dimensional equilibrium code is described and its results are checked against a two-dimensional equilibrium code; in Sec. III an even simpler analytic calculation is presented.
RFDR with Adiabatic Inversion Pulses: Application to Internuclear Distance Measurements
International Nuclear Information System (INIS)
Leppert, Joerg; Ohlenschlaeger, Oliver; Goerlach, Matthias; Ramachandran, Ramadurai
2004-01-01
In the context of the structural characterisation of biomolecular systems via MAS solid state NMR, the potential utility of homonuclear dipolar recoupling with adiabatic inversion pulses has been assessed via numerical simulations and experimental measurements. The results obtained suggest that it is possible to obtain reliable estimates of internuclear distances via an analysis of the initial cross-peak intensity buildup curves generated from two-dimensional adiabatic inversion pulse driven longitudinal magnetisation exchange experiments
Scattering theory of infrared divergent Pauli-Fierz Hamiltonians
Derezinski, J
2003-01-01
We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz Hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called {\\em coherent sectors} describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of {\\em inclusive and non-inclusive scattering cross-sections} for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.
Spectral properties of almost-periodic Hamiltonians
International Nuclear Information System (INIS)
Lima, R.
1983-12-01
We give a description of some spectral properties of almost-periodic hamiltonians. We put the stress on some particular points of the proofs of the existence of absolutely continuous or pure point spectrum [fr
Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2011-01-01
In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. -- Highlights: → Zero level set of Hamiltonian of Bianchi VIII/IX systems contains no periodic orbits. → Similar conditions for homoclinic/heteroclinic orbits are given. → General nonexistence conditions of compact invariant sets are got.
Compact invariant sets of the Bianchi VIII and Bianchi IX Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: konst@citedi.mx [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)
2011-08-22
In this Letter we prove that all compact invariant sets of the Bianchi VIII Hamiltonian system are contained in the set described by several simple linear equalities and inequalities. Moreover, we describe invariant domains in which the phase flow of this system has no recurrence property and show that there are no periodic orbits and neither homoclinic, nor heteroclinic orbits contained in the zero level set of its Hamiltonian. Similar results are obtained for the Bianchi IX Hamiltonian system. -- Highlights: → Zero level set of Hamiltonian of Bianchi VIII/IX systems contains no periodic orbits. → Similar conditions for homoclinic/heteroclinic orbits are given. → General nonexistence conditions of compact invariant sets are got.
International Nuclear Information System (INIS)
Abrashkevich, A.G.; Puzynin, I.V.; Vinitskij, S.I.
1997-01-01
A FORTRAN 77 program is presented which calculates asymptotics of potential curves and adiabatic potentials with an accuracy of O(ρ -2 ) in the framework of the hyperspherical adiabatic (HSA) approach. It is shown that matrix elements of the equivalent operator corresponding to the perturbation ρ -2 have a simple form in the basis of the Coulomb parabolic functions in the body-fixed frame and can be easily computed for high values of total orbital momentum and threshold number. The second-order corrections to the adiabatic curves are obtained as the solutions of the corresponding secular equation. The asymptotic potentials obtained can be used for the calculation of the energy levels and radial wave functions of two-electron systems in the adiabatic and coupled-channel approximations of the HSA approach
On time-dependent Hamiltonian realizations of planar and nonplanar systems
Esen, Oğul; Guha, Partha
2018-04-01
In this paper, we elucidate the key role played by the cosymplectic geometry in the theory of time dependent Hamiltonian systems in 2 D. We generalize the cosymplectic structures to time-dependent Nambu-Poisson Hamiltonian systems and corresponding Jacobi's last multiplier for 3 D systems. We illustrate our constructions with various examples.
Self-adjoint Hamiltonians with a mass jump: General matching conditions
International Nuclear Information System (INIS)
Gadella, M.; Kuru, S.; Negro, J.
2007-01-01
The simplest position-dependent mass Hamiltonian in one dimension, where the mass has the form of a step function with a jump discontinuity at one point, is considered. The most general matching conditions at the jumping point for the solutions of the Schroedinger equation that provide a self-adjoint Hamiltonian are characterized
Directory of Open Access Journals (Sweden)
Golubev Stanislav Sergeevich
2012-12-01
The effects of different climatic impacts lead to the deformation of glasses within an IGU (and its vertical cavity, respectively. Deformation of glasses and vertical cavities reduces the thermal resistance of an IGU. A numerical simulation of conjugate heat transfer within an IGU was implemented as part of the research into this phenomenon. Calculations were performed in ANSYS FLUENT CFD package. Basic equations describing the conservation of mass, conservation of momentum (in the Boussinesq approximation, conservation of energy were solved. Also, the radiation of the cavity wall was taken into account. Vertical walls were considered as non-isothermal, while horizontal walls were adiabatic. Calculations were made for several patterns of glass deformations. Calculation results demonstrate that the heat flow over vertical walls intensifies as the distance between centres of IGU glasses is reduced. The temperature in the central area of the hot glass drops.
Instability in Hamiltonian systems
Directory of Open Access Journals (Sweden)
A. Pumarino
2005-11-01
Besides proving the existence of Arnold diffusion for a new family of three degrees of freedom Hamiltonian systems, another goal of this book is not only to show how Arnold-like results can be extended to substantially larger sets of parameters, but also how to obtain effective estimates on the splitting of separatrices size when the frequency of the perturbation belongs to open real sets.
Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation
Bastero-Gil, Mar; Berera, Arjun; Ramos, Rudnei O.; Rosa, João G.
2018-02-01
We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.
Integrable quadratic classical Hamiltonians on so(4) and so(3, 1)
International Nuclear Information System (INIS)
Sokolov, Vladimir V; Wolf, Thomas
2006-01-01
We investigate a special class of quadratic Hamiltonians on so(4) and so(3, 1) and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree
Post-adiabatic analysis of atomic collisions
International Nuclear Information System (INIS)
Klar, H.; Fano, U.
1976-01-01
The coupling between adiabatic channels can be partially transformed away. The transformation need not induce any transition between channnels; but it correlates the radial wave functions and their gradients with the channel functions and it depresses the lower effective potentials, as the energy increases, in accordance with empirical evidence
A possible method for non-Hermitian and Non-PT-symmetric Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Jun-Qing Li
Full Text Available A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution are found not to be altered by the noncommutativity.
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
International Nuclear Information System (INIS)
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables
International Nuclear Information System (INIS)
Yang, Y.; Tan, G.Y.; Chen, P.X.; Zhang, Q.M.
2012-01-01
The adiabatic shear susceptibility of 2195 aluminum–lithium alloy was investigated by means of split Hopkinson pressure bar. The stress collapse in true stress–true strain curves and true stress–time curves was observed. The adiabatic shear susceptibility of different aging statuses and strain rate were discussed by means of metallography observation. The critical strain, stress collapse time and formation energy of adiabatic shear bands were compared. The results show that different aging statuses and strain rate have significant influences on adiabatic shear behaviors of 2195 aluminum–lithium alloy. The peak-aged specimen has the highest adiabatic shearing susceptibility, while the under-aged specimen has the least adiabatic shear susceptibility. The susceptibility of adiabatic shearing increases with the increases of strain rate.
Energy Technology Data Exchange (ETDEWEB)
Yang, Y. [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); State Key Laboratory of Explosion Science and Technology, Beijing 100081 (China); Tan, G.Y., E-mail: yangyanggroup@163.com [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); Chen, P.X. [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); Zhang, Q.M. [State Key Laboratory of Explosion Science and Technology, Beijing 100081 (China)
2012-06-01
The adiabatic shear susceptibility of 2195 aluminum-lithium alloy was investigated by means of split Hopkinson pressure bar. The stress collapse in true stress-true strain curves and true stress-time curves was observed. The adiabatic shear susceptibility of different aging statuses and strain rate were discussed by means of metallography observation. The critical strain, stress collapse time and formation energy of adiabatic shear bands were compared. The results show that different aging statuses and strain rate have significant influences on adiabatic shear behaviors of 2195 aluminum-lithium alloy. The peak-aged specimen has the highest adiabatic shearing susceptibility, while the under-aged specimen has the least adiabatic shear susceptibility. The susceptibility of adiabatic shearing increases with the increases of strain rate.
Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions
Cresson, Jacky; Pierret, Frédéric
2015-01-01
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.
Super Hamiltonian structure of the even order SKP hierarchy without reduction
International Nuclear Information System (INIS)
Watanabe, Yoshihide
1987-01-01
The super Hamiltonian operator which is different from that of Manin and Radul is derived from the even order SKP hierarchy without reduction and in terms of the operator, the equation in the hierarchy is written in a Hamiltonian form. (orig.)
From GCM energy kernels to Weyl-Wigner Hamiltonians: a particular mapping
International Nuclear Information System (INIS)
Galetti, D.
1984-01-01
A particular mapping is established which directly connects GCM energy kernels to Weyl-Wigner Hamiltonians, under the assumption of gaussian overlap kernel. As an application of this mapping scheme the collective Hamiltonians for some giant resonances are derived. (Author) [pt
International Nuclear Information System (INIS)
Kanungo, Jitendra; Dasgupta, S.
2014-01-01
We analyze the energy performance of a complete adiabatic circuit/system including the Power Clock Generator (PCG) at the 90 nm CMOS technology node. The energy performance in terms of the conversion efficiency of the PCG is extensively carried out under the variations of supply voltage, process corner and the driver transistor's width. We propose an energy-efficient singe cycle control circuit based on the two-stage comparator for the synchronous charge recovery sinusoidal power clock generator (PCG). The proposed PCG is used to drive the 4-bit adiabatic Ripple Carry Adder (RCA) and their simulation results are compared with the adiabatic RCA driven by the reported PCG. We have also simulated the logically equivalent static CMOS RCA circuit to compare the energy saving of adiabatic and non-adiabatic logic circuits. In the clock frequency range from 25 MHz to 1GHz, the proposed PCG gives a maximum conversion efficiency of 56.48%. This research work shows how the design of an efficient PCG increases the energy saving of adiabatic logic. (semiconductor integrated circuits)
Thermal reservoir sizing for adiabatic compressed air energy storage
Energy Technology Data Exchange (ETDEWEB)
Kere, Amelie; Goetz, Vincent; Py, Xavier; Olives, Regis; Sadiki, Najim [Perpignan Univ. (France). PROMES CNRS UPR 8521; Mercier-Allart, Eric [EDF R et D, Chatou (France)
2012-07-01
Despite the operation of the two existing industrial facilities to McIntosh (Alabama), and for more than thirty years, Huntorf (Germany), electricity storage in the form of compressed air in underground cavern (CAES) has not seen the development that was expected in the 80s. The efficiency of this form of storage was with the first generation CAES, less than 50%. The evolving context technique can significantly alter this situation. The new generation so-called Adiabatic CAES (A-CAES) is to retrieve the heat produced by the compression via thermal storage, thus eliminating the necessity of gas to burn and would allow consideration efficiency overall energy of the order of 70%. To date, there is no existing installation of A-CAES. Many studies describe the principal and the general working mode of storage systems by adiabatic compression of air. So, efficiencies of different configurations of adiabatic compression process were analyzed. The aim of this paper is to simulate and analyze the performances of a thermal storage reservoir integrated in the system and adapted to the working conditions of a CAES.
Simulation and analysis of different adiabatic Compressed Air Energy Storage plant configurations
International Nuclear Information System (INIS)
Hartmann, Niklas; Vöhringer, O.; Kruck, C.; Eltrop, L.
2012-01-01
Highlights: ► We modeled several configurations of an adiabatic Compressed Air Energy Storage (CAES) plant. ► We analyzed changes in efficiency of these configurations under varying operating conditions. ► The efficiency of the adiabatic CAES plant can reach about 70% for the isentropic configuration. ► In the polytropic case, the efficiency is about 10% lower (at about 60%) than in the isentropic configuration. ► The efficiency is highest for a two-stage CAES configuration and highly dependent on the cooling and heating demand. - Abstract: In this paper, the efficiency of one full charging and discharging cycle of several adiabatic Compressed Air Energy Storage (CAES) configurations are analyzed with the help of an energy balance. In the second step main driving factors for the efficiency of the CAES configurations are examined with the help of sensitivity analysis. The results show that the efficiency of the polytropic configuration is about 60%, which is considerable lower than literature values of an adiabatic CAES of about 70%. The high value of 70% is only reached for the isentropic (ideal) configuration. Key element to improve the efficiency is to develop high temperature thermal storages (>600 °C) and temperature resistant materials for compressors. The highest efficiency is delivered by the two-stage adiabatic CAES configuration. In this case the efficiency varies between 52% and 62%, depending on the cooling and heating demand. If the cooling is achieved by natural sources (such as a river), a realistic estimation of the efficiency of adiabatic Compressed Air Energy Storages (without any greenhouse gas emissions due to fuel consumption) is about 60%.
A progressive diagonalization scheme for the Rabi Hamiltonian
International Nuclear Information System (INIS)
Pan, Feng; Guan, Xin; Wang, Yin; Draayer, J P
2010-01-01
A diagonalization scheme for the Rabi Hamiltonian, which describes a qubit interacting with a single-mode radiation field via a dipole interaction, is proposed. It is shown that the Rabi Hamiltonian can be solved almost exactly using a progressive scheme that involves a finite set of one variable polynomial equations. The scheme is especially efficient for the lower part of the spectrum. Some low-lying energy levels of the model with several sets of parameters are calculated and compared to those provided by the recently proposed generalized rotating-wave approximation and a full matrix diagonalization.
Divide and conquer approach to quantum Hamiltonian simulation
Hadfield, Stuart; Papageorgiou, Anargyros
2018-04-01
We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.
Hamiltonian cycles in polyhedral maps
Indian Academy of Sciences (India)
We present a necessary and sufficient condition for existence of a contractible, non-separating and non-contractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces.We also present algorithms to construct such cycles whenever it exists where one of them is linear time and another is ...
Adiabatic translation factors in slow ion-atom collisions
International Nuclear Information System (INIS)
Vaaben, J.; Taulbjerg, K.
1981-01-01
The general properties of translation factors in slow atomic collisions are discussed. It is emphasised that an acceptable form of translation factors must be conceptually consistent with the basic underlying assumption of the molecular model; i.e. translation factors must relax adiabatically at intermediate and small internuclear separations. A simple physical argument is applied to derive a general parameter-free expression for the translation factor pertinent to an electron in a two-centre Coulomb field. Within the present approach the adiabatic translation factor is considered to be a property of the two-centre field independently of the molecular state under consideration. The generalisation to many-electron systems is therefore readily made. (author)
Lie transforms and their use in Hamiltonian perturbation theory
International Nuclear Information System (INIS)
Cary, J.R.
1978-06-01
A review is presented of the theory of Lie transforms as applied to Hamiltonian systems. We begin by presenting some general background on the Hamiltonian formalism and by introducing the operator notation for canonical transformations. We then derive the general theory of Lie transforms. We derive the formula for the new Hamiltonian when one uses a Lie transform to effect a canonical transformation, and we use Lie transforms to prove a very general version of Noether's theorem, or the symmetry-equals-invariant theorem. Next we use the general Lie transform theory to derive Deprit's perturbation theory. We illustrate this perturbation theory by application to two well-known problems in classical mechanics. Finally we present a chapter on conventions. There are many ways to develop Lie transforms. The last chapter explains the reasons for the choices made here
Optimal control of the power adiabatic stroke of an optomechanical heat engine.
Bathaee, M; Bahrampour, A R
2016-08-01
We consider the power adiabatic stroke of the Otto optomechanical heat engine introduced in Phys. Rev. Lett. 112, 150602 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.150602. We derive the maximum extractable work of both optomechanical normal modes in the minimum time while the system experiences quantum friction effects. We show that the total work done by the system in the power adiabatic stroke is optimized by a bang-bang control. The time duration of the power adiabatic stroke is of the order of the inverse of the effective optomechanical-coupling coefficient. The optimal phase-space trajectory of the Otto cycle for both optomechanical normal modes is also obtained.
Naz, Rehana
2018-01-01
Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.
Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example
Devi, Y. D.; Kota, V. K. B.
1993-07-01
A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150Nd.
Simple model for deriving sdg interacting boson model Hamiltonians: 150Nd example
International Nuclear Information System (INIS)
Devi, Y.D.; Kota, V.K.B.
1993-01-01
A simple and yet useful model for deriving sdg interacting boson model (IBM) Hamiltonians is to assume that single-boson energies derive from identical particle (pp and nn) interactions and proton, neutron single-particle energies, and that the two-body matrix elements for bosons derive from pn interaction, with an IBM-2 to IBM-1 projection of the resulting p-n sdg IBM Hamiltonian. The applicability of this model in generating sdg IBM Hamiltonians is demonstrated, using a single-j-shell Otsuka-Arima-Iachello mapping of the quadrupole and hexadecupole operators in proton and neutron spaces separately and constructing a quadrupole-quadrupole plus hexadecupole-hexadecupole Hamiltonian in the analysis of the spectra, B(E2)'s, and E4 strength distribution in the example of 150 Nd
Quantum trajectories for time-dependent adiabatic master equations
Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.
2018-02-01
We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.
International Nuclear Information System (INIS)
Prokhorov, L.V.
1982-01-01
Problems related to consideration of operator nonpermutability in Hamiltonian path integral (HPI) are considered in the review. Integrals are investigated using trajectories in configuration space (nonrelativistic quantum mechanics). Problems related to trajectory integrals in HPI phase space are discussed: the problem of operator nonpermutability consideration (extra terms problem) and corresponding equivalence rules; ambiguity of HPI usual recording; transition to curvilinear coordinates. Problem of quantization of dynamical systems with couplings has been studied. As in the case of canonical transformations, quantization of the systems with couplings of the first kind requires the consideration of extra terms
Large-scale stochasticity in Hamiltonian systems
International Nuclear Information System (INIS)
Escande, D.F.
1982-01-01
Large scale stochasticity (L.S.S.) in Hamiltonian systems is defined on the paradigm Hamiltonian H(v,x,t) =v 2 /2-M cos x-P cos k(x-t) which describes the motion of one particle in two electrostatic waves. A renormalization transformation Tsub(r) is described which acts as a microscope that focusses on a given KAM (Kolmogorov-Arnold-Moser) torus in phase space. Though approximate, Tsub(r) yields the threshold of L.S.S. in H with an error of 5-10%. The universal behaviour of KAM tori is predicted: for instance the scale invariance of KAM tori and the critical exponent of the Lyapunov exponent of Cantori. The Fourier expansion of KAM tori is computed and several conjectures by L. Kadanoff and S. Shenker are proved. Chirikov's standard mapping for stochastic layers is derived in a simpler way and the width of the layers is computed. A simpler renormalization scheme for these layers is defined. A Mathieu equation for describing the stability of a discrete family of cycles is derived. When combined with Tsub(r), it allows to prove the link between KAM tori and nearby cycles, conjectured by J. Greene and, in particular, to compute the mean residue of a torus. The fractal diagrams defined by G. Schmidt are computed. A sketch of a methodology for computing the L.S.S. threshold in any two-degree-of-freedom Hamiltonian system is given. (Auth.)
Redesign of the DFT/MRCI Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Lyskov, Igor; Kleinschmidt, Martin; Marian, Christel M., E-mail: Christel.Marian@hhu.de [Institute of Theoretical and Computational Chemistry, Heinrich-Heine-University Düsseldorf, Universitätsstraße 1, 40225 Düsseldorf (Germany)
2016-01-21
The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.
The multiphonon method as a dynamical approach to octupole correlations in deformed nuclei
International Nuclear Information System (INIS)
Piepenbring, R.
1986-09-01
The octupole correlations in nuclei are studied within the framework of the multiphonon method which is mainly the exact diagonalization of the total Hamiltonian in the space spanned by collective phonons. This treatment takes properly into account the Pauli principle. It is a microscopic approach based on a reflection symmetry of the potential. The spectroscopic properties of double even and odd-mass nuclei are nicely reproduced. The multiphonon method appears as a dynamical approach to octupole correlations in nuclei which can be compared to other models based on stable octupole deformation. 66 refs
A Monte Carlo procedure for Hamiltonians with small nonlocal correction terms
International Nuclear Information System (INIS)
Mack, G.; Pinn, K.
1986-03-01
We consider lattice field theories whose Hamiltonians contain small nonlocal correction terms. We propose to do simulations for an auxiliarly polymer system with field dependent activities. If a nonlocal correction term to the Hamiltonian is small, it need to be evaluated only rarely. (orig.)
Hamiltonian cycle problem and Markov chains
Borkar, Vivek S; Filar, Jerzy A; Nguyen, Giang T
2014-01-01
This book summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian cycle and the Travelling Salesman problems - into convex domains where continuum analysis can be carried out.
Variable Delay in port-Hamiltonian Telemanipulation
Secchi, C; Stramigioli, Stefano; Fantuzzi, C.
2006-01-01
In several applications involving bilateral telemanipulation, master and slave act at different power scales. In this paper a strategy for passively dealing with variable communication delay in scaled port-Hamiltonian based telemanipulation over packet switched networks is proposed.
Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods
Directory of Open Access Journals (Sweden)
Tetsuya Misawa
2010-01-01
Full Text Available “Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods” proposed by Misawa (2001. In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.
Adiabatic theory of ionization of atoms by intense laser pulses
International Nuclear Information System (INIS)
Tolstikhin, Oleg I; Morishita, Toru; Watanabe, Shinichi
2009-01-01
As a first step towards the adiabatic theory of ionization of atoms by intense laser pulses, here we consider the simplest one-dimensional zero-range potential model. The asymptotic solution to the time-dependent Schroedinger equation in the adiabatic regime is obtained and the photoelectron spectrum is calculated. The factorization formula for the photoelectron spectrum in the back-rescattering region, first suggested by Morishita et al. [Phys. Rev. Lett. 100, 013903 (2008)] on the basis of ab initio calculations, is derived analytically.
Symplectic and Hamiltonian structures of nonlinear evolution equations
International Nuclear Information System (INIS)
Dorfman, I.Y.
1993-01-01
A Hamiltonian structure on a finite-dimensional manifold can be introduced either by endowing it with a (pre)symplectic structure, or by describing the Poisson bracket with the help of a tensor with two upper indices named the Poisson structure. Under the assumption of nondegeneracy, the Poisson structure is nothing else than the inverse of the symplectic structure. Also in the degenerate case the distinction between the two approaches is almost insignificant, because both presymplectic and Poisson structures split into symplectic structures on leaves of appropriately chosen foliations. Hamiltonian structures that arise in the theory of evolution equations demonstrate something new in this respect: trying to operate in local terms, one is induced to develop both approaches independently. Hamiltonian operators, being the infinite-dimensional counterparts of Poisson structures, were the first to become the subject of investigations. A considerable period of time passed before the papers initiated research in the theory of symplectic operators, being the counterparts of presymplectic structures. In what follows, we focus on the main achievements in this field
Chen, Yunjie; Kale, Seyit; Weare, Jonathan; Dinner, Aaron R; Roux, Benoît
2016-04-12
A multiple time-step integrator based on a dual Hamiltonian and a hybrid method combining molecular dynamics (MD) and Monte Carlo (MC) is proposed to sample systems in the canonical ensemble. The Dual Hamiltonian Multiple Time-Step (DHMTS) algorithm is based on two similar Hamiltonians: a computationally expensive one that serves as a reference and a computationally inexpensive one to which the workload is shifted. The central assumption is that the difference between the two Hamiltonians is slowly varying. Earlier work has shown that such dual Hamiltonian multiple time-step schemes effectively precondition nonlinear differential equations for dynamics by reformulating them into a recursive root finding problem that can be solved by propagating a correction term through an internal loop, analogous to RESPA. Of special interest in the present context, a hybrid MD-MC version of the DHMTS algorithm is introduced to enforce detailed balance via a Metropolis acceptance criterion and ensure consistency with the Boltzmann distribution. The Metropolis criterion suppresses the discretization errors normally associated with the propagation according to the computationally inexpensive Hamiltonian, treating the discretization error as an external work. Illustrative tests are carried out to demonstrate the effectiveness of the method.
Development of a model for dimethyl ether non-adiabatic reactors to improve methanol conversion
Energy Technology Data Exchange (ETDEWEB)
Nasrollahi, Fatemeh [University of Tehran, Tehran (Iran, Islamic Republic of); Bakeri, Gholamreza; Rahimnejad, Mostafa [Babol Noshirvani University of Technology, Babol (Iran, Islamic Republic of); Ismail, Ahmad Fauzi [Universiti Teknologi Malaysia, Skudai (Malaysia); Imanian, Mahdi [Mohajer Technical University, Isfahan (Iran, Islamic Republic of)
2013-10-15
The modeling of adiabatic and non-adiabatic reactors, using three cooling mediums in the shell side of a shell and tube reactor in cocurrent and countercurrent flow regimes has been conducted. The cooling mediums used in this research are saturated water and methanol feed gas to a reactor which is preheated in the shell side and a special type of oil. The results of adiabatic reactor modeling show good compatibility with the data received from a commercial plant. The results of non-adiabatic reactor modeling showed that more methanol conversion can be achieved in a lower length of reactor, even though in some cases the maximum temperature in the tube side of the reactor is more than the deactivation temperature of the catalyst.
Classical mechanics Hamiltonian and Lagrangian formalism
Deriglazov, Alexei
2016-01-01
This account of the fundamentals of Hamiltonian mechanics also covers related topics such as integral invariants and the Noether theorem. With just the elementary mathematical methods used for exposition, the book is suitable for novices as well as graduates.
Solving a Hamiltonian Path Problem with a bacterial computer
Directory of Open Access Journals (Sweden)
Treece Jessica
2009-07-01
Full Text Available Abstract Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node
Solving a Hamiltonian Path Problem with a bacterial computer
Baumgardner, Jordan; Acker, Karen; Adefuye, Oyinade; Crowley, Samuel Thomas; DeLoache, Will; Dickson, James O; Heard, Lane; Martens, Andrew T; Morton, Nickolaus; Ritter, Michelle; Shoecraft, Amber; Treece, Jessica; Unzicker, Matthew; Valencia, Amanda; Waters, Mike; Campbell, A Malcolm; Heyer, Laurie J; Poet, Jeffrey L; Eckdahl, Todd T
2009-01-01
Background The Hamiltonian Path Problem asks whether there is a route in a directed graph from a beginning node to an ending node, visiting each node exactly once. The Hamiltonian Path Problem is NP complete, achieving surprising computational complexity with modest increases in size. This challenge has inspired researchers to broaden the definition of a computer. DNA computers have been developed that solve NP complete problems. Bacterial computers can be programmed by constructing genetic circuits to execute an algorithm that is responsive to the environment and whose result can be observed. Each bacterium can examine a solution to a mathematical problem and billions of them can explore billions of possible solutions. Bacterial computers can be automated, made responsive to selection, and reproduce themselves so that more processing capacity is applied to problems over time. Results We programmed bacteria with a genetic circuit that enables them to evaluate all possible paths in a directed graph in order to find a Hamiltonian path. We encoded a three node directed graph as DNA segments that were autonomously shuffled randomly inside bacteria by a Hin/hixC recombination system we previously adapted from Salmonella typhimurium for use in Escherichia coli. We represented nodes in the graph as linked halves of two different genes encoding red or green fluorescent proteins. Bacterial populations displayed phenotypes that reflected random ordering of edges in the graph. Individual bacterial clones that found a Hamiltonian path reported their success by fluorescing both red and green, resulting in yellow colonies. We used DNA sequencing to verify that the yellow phenotype resulted from genotypes that represented Hamiltonian path solutions, demonstrating that our bacterial computer functioned as expected. Conclusion We successfully designed, constructed, and tested a bacterial computer capable of finding a Hamiltonian path in a three node directed graph. This proof
General formalism of Hamiltonians for realizing a prescribed evolution of a qubit
International Nuclear Information System (INIS)
Tong, D.M.; Chen, J.-L.; Lai, C.H.; Oh, C.H.; Kwek, L.C.
2003-01-01
We investigate the inverse problem concerning the evolution of a qubit system, specifically we consider how one can establish the Hamiltonians that account for the evolution of a qubit along a prescribed path in the projected Hilbert space. For a given path, there are infinite Hamiltonians which can realize the same evolution. A general form of the Hamiltonians is constructed in which one may select the desired one for implementing a prescribed evolution. This scheme can be generalized to higher dimensional systems
Mid-range adiabatic wireless energy transfer via a mediator coil
International Nuclear Information System (INIS)
Rangelov, A.A.; Vitanov, N.V.
2012-01-01
A technique for efficient mid-range wireless energy transfer between two coils via a mediator coil is proposed. By varying the coil frequencies, three resonances are created: emitter–mediator (EM), mediator–receiver (MR) and emitter–receiver (ER). If the frequency sweeps are adiabatic and such that the EM resonance precedes the MR resonance, the energy flows sequentially along the chain emitter–mediator–receiver. If the MR resonance precedes the EM resonance, then the energy flows directly from the emitter to the receiver via the ER resonance; then the losses from the mediator are suppressed. This technique is robust against noise, resonant constraints and external interferences. - Highlights: ► Efficient and robust mid-range wireless energy transfer via a mediator coil. ► The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. ► Wireless energy transfer is insensitive to any resonant constraints. ► Wireless energy transfer is insensitive to noise in the neighborhood of the coils.
Dynamics of ionizing shock waves on adiabatic motions of gases
International Nuclear Information System (INIS)
Zorev, N.N.; Sklizkov, G.V.; Shikanov, A.S.
1982-01-01
Results are presented of an experimental investigation of free (adiabatic) motion of a spherical ionizing wave in deuterium produced by an expanding laser plasma. It is shown that the discrepancy between the free movement of shock waves (which lead to total ionization of the gas) and the Sedov-Taylor model of a spontaneous point explosion is not related to variations in the adiabat exponent γ and the motion occurs for a constant γ=5/3. The effect is ascribed to the influence of the shock wave front structure on the dynamics of its propagation. An analytic expression for the motion of symmetric ionizing shock waves is found which has an accuracy of better than 1%. As a result the adiabat exponent was determined experimentally. A method for determining the energy of a shock wave on the basis of its dynamics of motion is developed which has an accuracy of approximately 5% [ru
Multi-Hamiltonian structure of Lotka-Volterra and quantum Volterra models
International Nuclear Information System (INIS)
Cronstroem, C.; Noga, M.
1995-01-01
We consider evolution equations of the Lotka-Volterra type, and elucidate especially their formulation as canonical Hamiltonian systems. The general conditions under which these equations admit several conserved quantities (multi-Hamiltonians) are analysed. A special case, which is related to the Liouville model on a lattice, is considered in detail, both as a classical and as a quantum system. (orig.)
On the time evolution operator for time-dependent quadratic Hamiltonians
International Nuclear Information System (INIS)
Fernandez, F.M.
1989-01-01
The Schroedinger equation with a time-dependent quadratic Hamiltonian is investigated. The time-evolution operator is written as a product of exponential operators determined by the Heisenberg equations of motion. This product operator is shown to be global in the occupation number representation when the Hamiltonian is Hermitian. The success of some physical applications of the product-form representation is explained
Purely non-local Hamiltonian formalism, Kohno connections and ∨-systems
International Nuclear Information System (INIS)
Arsie, Alessandro; Lorenzoni, Paolo
2014-01-01
In this paper, we extend purely non-local Hamiltonian formalism to a class of Riemannian F-manifolds, without assumptions on the semisimplicity of the product ○ or on the flatness of the connection ∇. In the flat case, we show that the recurrence relations for the principal hierarchy can be re-interpreted using a local and purely non-local Hamiltonian operators and in this case they split into two Lenard-Magri chains, one involving the even terms, the other involving the odd terms. Furthermore, we give an elementary proof that the Kohno property and the ∨-system condition are equivalent under suitable assumptions and we show how to associate a purely non-local Hamiltonian structure to any ∨-system, including degenerate ones
Spontaneous symmetry breaking and neutral stability in the noncanonical Hamiltonian formalism
International Nuclear Information System (INIS)
Morrison, P.J.; Eliezer, S.
1985-10-01
The noncanonical Hamiltonian formalism is based upon a generalization of the Poisson bracket, a particular form of which is possessed by continuous media fields. Associated with this generalization are special constants of motion called Casimirs. These are constants that can be viewed as being built into the phase space, for they are invariant for all Hamiltonians. Casimirs are important because when added to the Hamiltonian they yield an effective Hamiltonian that produces equilibrium states upon variation. The stability of these states can be ascertained by a second variation. Goldstone's theorem, in its usual context, determines zero eigenvalues of the mass matrix for a given vacuum state, the equilibrium with minimum energy. Here, since for fluids and plasmas the vacuum state is uninteresting, we examine symmetry breaking for general equilibria. Broken symmetries imply directions of neutral stability. Two examples are presented: the nonlinear Alfven wave of plasma physics and the Korteweg-de Vries soliton. 46 refs
Hamiltonian formulation of the supermembrane
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Tanii, Y.
1987-06-01
The Hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence free 2-vectors are unfixed. (author). 10 refs
Hamiltonian thermodynamics of charged three-dimensional dilatonic black holes
International Nuclear Information System (INIS)
Dias, Goncalo A. S.; Lemos, Jose P. S.
2008-01-01
The action for a class of three-dimensional dilaton-gravity theories, with an electromagnetic Maxwell field and a cosmological constant, can be recast in a Brans-Dicke-Maxwell type action, with its free ω parameter. For a negative cosmological constant, these theories have static, electrically charged, and spherically symmetric black hole solutions. Those theories with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity (ω→±∞), a dimensionally reduced cylindrical four-dimensional general relativity theory (ω=0), and a theory representing a class of theories (ω=-3), all with a Maxwell term. The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti-de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces and the radial component of the vector potential one-form are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with two pairs of canonical coordinates (M,P M ;Q,P Q ), where M is the mass parameter, which for ω M is the conjugate momenta of M, Q is the charge parameter, and P Q is its conjugate momentum. The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schroedinger evolution operator is constructed, the trace is taken, and the partition function of the grand canonical ensemble is obtained, where the chemical potential is the scalar electric field φ. Like the uncharged cases studied previously, the charged black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.
Accuracy of the adiabatic-impulse approximation for closed and open quantum systems
Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo
2018-03-01
We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.
Hamiltonian formulation of reduced magnetohydrodynamics
International Nuclear Information System (INIS)
Morrison, P.J.; Hazeltine, R.D.
1983-07-01
Reduced magnetohydrodynamics (RMHD) has become a principal tool for understanding nonlinear processes, including disruptions, in tokamak plasmas. Although analytical studies of RMHD turbulence have been useful, the model's impressive ability to simulate tokamak fluid behavior has been revealed primarily by numerical solution. The present work describes a new analytical approach, not restricted to turbulent regimes, based on Hamiltonian field theory. It is shown that the nonlinear (ideal) RMHD system, in both its high-beta and low-beta versions, can be expressed in Hanmiltonian form. Thus a Poisson bracket, [ , ], is constructed such that each RMHD field quantitity, xi/sub i/, evolves according to xi/sub i/ = [xi/sub i/,H], where H is the total field energy. The new formulation makes RMHD accessible to the methodology of Hamiltonian mechanics; it has lead, in particular, to the recognition of new RMHD invariants and even exact, nonlinear RMHD solutions. A canonical version of the Poisson bracket, which requires the introduction of additional fields, leads to a nonlinear variational principle for time-dependent RMHD
Directory of Open Access Journals (Sweden)
Böyükata M.
2014-03-01
Full Text Available Quantum phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model with a description based on the concept of intrinsic states. We consider the case of a single j=9/2 odd-particle coupled to an even-even boson core that performs a transition from spherical to deformed prolate and to deformed gamma-unstable shapes varying a control parameter in the boson Hamiltonian. The effect of the coupling of the odd particle to this core is discussed along the shape transition and, in particular, at the critical point.
EBSD analysis of plastic deformation of copper foils by flexible pad laser shock forming
Energy Technology Data Exchange (ETDEWEB)
Nagarajan, Balasubramanian; Castagne, Sylvie [Nanyang Technological University, SIMTech-NTU Joint Laboratory (Precision Machining), Singapore (Singapore); Nanyang Technological University, School of Mechanical and Aerospace Engineering, Singapore (Singapore); Wang, Zhongke; Zheng, H.Y. [Nanyang Technological University, SIMTech-NTU Joint Laboratory (Precision Machining), Singapore (Singapore); Singapore Institute of Manufacturing Technology, Machining Technology Group, Singapore (Singapore)
2015-11-15
Flexible pad laser shock forming (FPLSF) is a new mold-free microforming process that induces high-strain-rate plastic deformation in thin metallic foils using laser-induced shock pressure and a hyperelastic flexible pad. This paper studies the plastic deformation behavior of copper foils formed through FPLSF by investigating surface hardness and microstructure. The microstructure of the foil surface before and after FPLSF is analyzed by electron backscatter diffraction technique using grain size distribution and grain boundary misorientation angle as analysis parameters. The surface hardness of the craters experienced a significant improvement after FPLSF; the top crater surface being harder than the bottom surface. The microstructure of the copper foil surface after FPLSF was found to be dominated by grain elongation, along with minor occurrences of subgrain formation, grain refinement, and high dislocation density regions. The results indicate that the prominent plastic deformation mechanism in FPLSF is strain hardening behavior rather than the typical adiabatic softening effect known to be occurring at high-strain-rates for processes such as electromagnetic forming, explosive forming, and laser shock forming. This significant difference in FPLSF is attributed to the concurrent reduction in plastic strain, strain rate, and the inertia effects, resulting from the FPLSF process configuration. Correspondingly, different deformation behaviors are experienced at top and bottom surfaces of the deformation craters, inducing the change in surface hardness and microstructure profiles. (orig.)
Functional integral and effective Hamiltonian t-J-V model of strongly correlated electron system
International Nuclear Information System (INIS)
Belinicher, V.I.; Chertkov, M.V.
1990-09-01
The functional integral representation for the generating functional of t-J-V model is obtained. In the case close to half filling this functional integral representation reduces the conventional Hamiltonian of t-J-V model to the Hamiltonian of the system containing holes and spins 1/2 at each lattice size. This effective Hamiltonian coincides with that one obtained one of the authors by different method. This Hamiltonian and its dynamical variables can be used for description of different magnetic phases of t-J-V model. (author). 16 refs
Necessary conditions for super-integrability of Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: maria.przybylska@astri.uni.torun.pl; Yoshida, Haruo [National Astronomical Observatory, 2-21-1 Osawa, Mitaka, 181-8588 Tokyo (Japan)], E-mail: h.yoshida@nao.ac.jp
2008-08-18
We formulate a general theorem which gives a necessary condition for the maximal super-integrability of a Hamiltonian system. This condition is expressed in terms of properties of the differential Galois group of the variational equations along a particular solution of the considered system. An application of this general theorem to natural Hamiltonian systems of n degrees of freedom with a homogeneous potential gives easily computable and effective necessary conditions for the super-integrability. To illustrate an application of the formulated theorems, we investigate: three known families of integrable potentials, and the three body problem on a line.
The intrinsic stochasticity of near-integrable Hamiltonian systems
Energy Technology Data Exchange (ETDEWEB)
Krlin, L [Ceskoslovenska Akademie Ved, Prague (Czechoslovakia). Ustav Fyziky Plazmatu
1989-09-01
Under certain conditions, the dynamics of near-integrable Hamiltonian systems appears to be stochastic. This stochasticity (intrinsic stochasticity, or deterministic chaos) is closely related to the Kolmogorov-Arnold-Moser (KAM) theorem of the stability of near-integrable multiperiodic Hamiltonian systems. The effect of the intrinsic stochasticity attracts still growing attention both in theory and in various applications in contemporary physics. The paper discusses the relation of the intrinsic stochasticity to the modern ergodic theory and to the KAM theorem, and describes some numerical experiments on related astrophysical and high-temperature plasma problems. Some open questions are mentioned in conclusion. (author).
Hamiltonian formulation of QCD in the Schwinger gauge
International Nuclear Information System (INIS)
Schutte, D.
1989-01-01
The structure of the Hamiltonian related to a regularized non-Abelian gauge field theory is discussed in the light of different choices for gauge-invariant wave functionals (loop space, Coulomb, axial, Schwinger gauge). Arguments are given for the suggestion that the Schwinger gauge offers a specially suited framework for the computation of bound-state (hadron) properties. The most important reasons are the manifest rotation invariance, the lack of a Gribov horizon (giving standard many-body techniques a better chance), and the fact that a regularization analogous to the lattice regularization is easily implementable. Some details of the Schwinger-gauge Hamiltonian theory are discussed
Quantum finance Hamiltonian for coupon bond European and barrier options.
Baaquie, Belal E
2008-03-01
Coupon bond European and barrier options are financial derivatives that can be analyzed in the Hamiltonian formulation of quantum finance. Forward interest rates are modeled as a two-dimensional quantum field theory and its Hamiltonian and state space is defined. European and barrier options are realized as transition amplitudes of the time integrated Hamiltonian operator. The double barrier option for a financial instrument is "knocked out" (terminated with zero value) if the price of the underlying instrument exceeds or falls below preset limits; the barrier option is realized by imposing boundary conditions on the eigenfunctions of the forward interest rates' Hamiltonian. The price of the European coupon bond option and the zero coupon bond barrier option are calculated. It is shown that, is general, the constraint function for a coupon bond barrier option can -- to a good approximation -- be linearized. A calculation using an overcomplete set of eigenfunctions yields an approximate price for the coupon bond barrier option, which is given in the form of an integral of a factor that results from the barrier condition times another factor that arises from the payoff function.
International Nuclear Information System (INIS)
Struckmeier, Juergen
2005-01-01
We will present a consistent description of Hamiltonian dynamics on the 'symplectic extended phase space' that is analogous to that of a time-independent Hamiltonian system on the conventional symplectic phase space. The extended Hamiltonian H 1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional Hamiltonian H will be derived from a generalized formulation of Hamilton's variational principle. The extended canonical transformation theory then naturally permits transformations that also map the time scales of the original and destination system, while preserving the extended Hamiltonian H 1 , and hence the form of the canonical equations derived from H 1 . The Lorentz transformation, as well as time scaling transformations in celestial mechanics, will be shown to represent particular canonical transformations in the symplectic extended phase space. Furthermore, the generalized canonical transformation approach allows us to directly map explicitly time-dependent Hamiltonians into time-independent ones. An 'extended' generating function that defines transformations of this kind will be presented for the time-dependent damped harmonic oscillator and for a general class of explicitly time-dependent potentials. In the appendix, we will re-establish the proper form of the extended Hamiltonian H 1 by means of a Legendre transformation of the extended Lagrangian L 1
On the adiabatic theorem in quantum statistical mechanics
International Nuclear Information System (INIS)
Narnhofer, H.; Thirring, W.
1982-01-01
We show that with suitable assumptions the equilibrium states are exactly the states invariant under adiabatic local perturbations. The relevance of this fact to the problem of ergodicity is discussed. (Author)