Showing papers on "Canonical transformation published in 2002"
TL;DR: In this article, the energy spectrum of the bound states and their wave functions are explicitly written down and mapped the wave equation for these systems into well-known exactly solvable Schrodinger equations with constant mass using point canonical transformation.
Abstract: Given a spatially dependent mass distribution, we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wave functions are written down explicitly. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger equations with constant mass using point canonical transformation. The Oscillator, Coulomb, and Morse class of potentials are considered.
284 citations
TL;DR: In this paper, a new approach for numerical solutions of ab initio quantum chemistry systems is presented, called canonical diagonalization, which diagonalizes directly the second-quantized Hamiltonian by a sequence of numerical canonical transformations.
Abstract: We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second-quantized Hamiltonian by a sequence of numerical canonical transformations.
118 citations
TL;DR: In this paper, a new approach for numerical solutions of ab initio quantum chemistry systems is presented, called canonical diagonalization, which diagonalizes directly the second quantized Hamiltonian by a sequence of numerical canonical transformations.
Abstract: We present a new approach for numerical solutions of ab initio quantum chemistry systems. The main idea of the approach, which we call canonical diagonalization, is to diagonalize directly the second quantized Hamiltonian by a sequence of numerical canonical transformations.
95 citations
TL;DR: In this article, a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS_2\times S^2 horizon of an extreme Reissner-Nordstrøm black hole was proposed.
Abstract: We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS_2\times S^2 horizon of an extreme Reissner-Nordstr\"om black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N=4 superparticle on AdS_2\times S^2 background.
89 citations
TL;DR: In this paper, the rest-frame instant form of tetrad gravity restricted to Christodoulou-Klainermann spacetimes was defined and solved by solving the multitemporal equations associated with the rotation and space diffeomorphism constraints.
Abstract: We define the rest-frame instant form of tetrad gravity restricted to Christodoulou-Klainermann spacetimes After a study of the Hamiltonian group of gauge transformations generated by the 14 first class constraints of the theory, we define and solve the multitemporal equations associated with the rotation and space diffeomorphism constraints, finding how the cotriads and their momenta depend on the corresponding gauge variables This allows to find a quasi-Shanmugadhasan canonical transformation to the class of 3-orthogonal gauges and to find the Dirac observables for superspace in these gauges The construction of the explicit form of the transformation and of the solution of the rotation and supermomentum constraints is reduced to solve a system of elliptic linear and quasi-linear partial differential equations We then show that the superhamiltonian constraint becomes the Lichnerowicz equation for the conformal factor of the 3-metric and that the last gauge variable is the momentum conjugated to the conformal factor The gauge transformations generated by the superhamiltonian constraint perform the transitions among the allowed foliations of spacetime, so that the theory is independent from its 3+1 splittings In the special 3-orthogonal gauge defined by the vanishing of the conformal factor momentum we determine the final Dirac observables for the gravitational field even if we are not able to solve the Lichnerowicz equation The final Hamiltonian is the weak ADM energy restricted to this completely fixed gauge
59 citations
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01 Dec 2002
TL;DR: In this paper, the group-geometrical structure of the Kepler problem was studied and it was shown that this structure also turns out to be useful in the study of the perturbed case.
Abstract: In this chapter, we will study the group-geometrical structure of the Kepler problem and point out how this structure also turns out to be useful in the study of the perturbed case.
55 citations
TL;DR: In this article, a new model of Hamiltonian which represents the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a cavity was introduced, which can be regarded as a generalization of the Jaynes-Cummings model.
46 citations
TL;DR: In this article, an exact invariant for n-degree-of-freedom non-relativistic Hamiltonian systems with general time-dependent potentials is derived, and the invariant can be expressed as an integral of an energy balance equation.
Abstract: An exact invariant is derived for n-degree-of-freedomnon-relativistic Ham iltonian sys- tems with general time-dependent potentials. To work out the invariant, an infinitesimal canonical transformation is performed in the framework of the extended phase-space. We apply this ap- proach to derive the invariant for a specific class of Hamiltonian systems. For the considered class of Hamiltonian systems, the invariant is obtained equivalently performing in the extended phase- space a finite canonical transformation of the initially time-dependent Hamiltonian to a time-inde- pendent one. It is furthermore shown that the invariant can be expressed as an integral of an energy balance equation. The invariant itself contains a time-dependent auxiliary function xðtÞ that represents a solution of a linear third-order differential equation, referred to as the auxiliary equation. The coefficients of the auxiliary equation depend in general on the explicitly known configuration space trajectory defined by the system's time evolution. This complexity of the auxiliary equation reflects the gen- erally involved phase-space symmetry associated with the conserved quantity of a time-dependent non-linear Hamiltonian system. Our results are applied to three examples of time-dependent damped and undamped oscillators. The known invariants for time-dependent and time-indepen- dent harmonic oscillators are shown to follow directly from our generalized formulation.
32 citations
TL;DR: In this paper, the guiding center motion of charged particles in a toroidal magnetic system has been studied using a cylindrical coordinate system instead of a magnetic coordinate system on which many conventional standard methods are based.
Abstract: A Hamiltonian method to study the guiding center motion of charged particles in a toroidal magnetic system has been developed. It uses a cylindrical coordinate system instead of a magnetic coordinate system on which many conventional standard methods are based. The six-dimensional (6D) Hamiltonian equations for the guiding center motion are derived by a canonical transformation of fast-oscillating variables to slowly varying ones which are guiding center coordinates. It is shown that one of these slowly varying variables, i.e., the action variable conjugated to the fast-oscillating gyrophase is an adiabatic invariant for the tokamak equilibrium magnetic field perturbed by the external time-dependent magnetic field. This allows to reduce the 6D Hamiltonian system to the 4D one. The method is valid for the study of the guiding center motion of particles in time-dependent magnetic and electric fields, especially, ergodic magnetic fields, where spatial and temporal scales of variation are much larger than the gyroradius and the gyroperiod.
21 citations
TL;DR: In this article, the authors develop an algebraic framework to show that a similar mapping procedure also exists between a class of non-central potentials, and discuss the inter-relation between the generalized Coulomb and oscillator systems.
Abstract: Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure also exists between a class of non-central potentials. As an illustrative example, we discuss the inter-relation between the generalized Coulomb and oscillator systems.
18 citations
TL;DR: In this article, the authors considered the canonical transformation of integrable systems in the space of coupling constants and gave explicit formulas for harmonic oscillator and for Calogero-Ruijsenaars-Dell system.
TL;DR: In this paper, it was shown that for a generalization to systems invariant under non-conventional time reversal, which also belong to the orthogonal symmetry class, it is necessary to redefine the configuration space by a suitable canonical transformation.
Abstract: Recently, Sieber and Richter calculated semiclassically a first off-diagonal contribution to the orthogonal form factor for a billiard on a surface of constant negative curvature. Following prior suggestions from the theory of disordered systems, they considered orbit pairs with almost the same action. For a generalization to systems invariant under non-conventional time reversal, which also belong to the orthogonal symmetry class, we show here that it is necessary to redefine the configuration space by a suitable canonical transformation; the distinction of this space is that it lets time reversal look conventional.
TL;DR: In this paper, a new method to generate symplectic diffeomorphisms based on primitive functions was described, and it was applied to the construction of normal forms of KAM tori, a concrete application, developed in detail and implemented numerically, is normal forms near invariant circles.
TL;DR: In this paper, a nonlinear canonical transformation is used to transform the rapidly oscillating terms in the original Hamiltonian to a new Hamiltonian that contains slowly varying terms only. And a stationary solution to the transformed Vlasov equation has been obtained.
Abstract: A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the dynamics of an intense beam propagating through a periodic focusing lattice, and to the coherent beam-beam interaction. A stationary solution to the transformed Vlasov equation has been obtained.
TL;DR: In this article, the canonical transformation of coordinates for a strong-coupled system of electron and phonon field was formulated for a bipolaron, taking into account the rigorous fulfillment of the conservation laws.
Abstract: The method of canonical transformation of coordinates is formulated for a strong-coupled system of electron and phonon field, taking into account the rigorous fulfillment of the conservation laws. The system of electronically excited terms of a bipolaron has been established. The sequence of the excited terms and their dependence on the distance between polarons have been obtained.
TL;DR: In this paper, a canonical transformation of the Hamiltonian is proposed to distinguish fast and slow variables, and the canonical coordinates of a collective mode are naturally introduced to explain the stability of these structures.
Abstract: The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low-energy initial conditions. The aim of this paper is to show in a detailed manner how these structures arise and to explain their stability. By a convenient canonical transformation we rewrite the Hamiltonian in such a way that fast and slow variables are singled out and the canonical coordinates of a collective mode are naturally introduced. If, initially, enough energy is put in this mode, its decay can be extremely slow. However, both analytical arguments and numerical simulations suggest that these structures eventually decay to the spatially uniform equilibrium state, although this can happen on impressively long time scales. Finally, we heuristically introduce a one-particle time-dependent Hamiltonian that well reproduces most of the observed phenomenology.
TL;DR: In this article, the authors consider the Hamiltonian dynamics of the collapse of an arbitrary distribution of null dust, expressed in terms of the physical radius R, the null coordinates, V for a collapsing cloud or U for an expanding cloud, the mass function m of the null matter, and their conjugate momenta.
Abstract: Spherically symmetric, null dust clouds, like their timelike counterparts, may collapse classically into black holes or naked singularities depending on their initial conditions. We consider the Hamiltonian dynamics of the collapse of an arbitrary distribution of null dust, expressed in terms of the physical radius R, the null coordinates, V for a collapsing cloud or U for an expanding cloud, the mass function m of the null matter, and their conjugate momenta. This description is obtained from the Arnowitt-Deser-Misner description by a Kucha\ifmmode \check{r}\else \v{r}\fi{}-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions to the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions.
TL;DR: In this article, a partial canonical transformation of the action recasts the problem in a coordinate system in which the natural boundary conditions at z = 0 are the angular positions and redshifts relative to a reference galaxy that may itself be in motion.
Abstract: In the standard formulation of cosmological action, the final-time boundary conditions are taken to be the three position coordinates of each galaxy at z = 0. It can be shown that a partial canonical transformation of the action recasts the problem in a coordinate system in which the natural boundary conditions at z = 0 are the angular positions and redshifts relative to a reference galaxy that may itself be in motion. Successful reconstruction of particle orbits back in time, as well as the correct prediction of cosmological parameters, are demonstrated for small systems of particles through conventional N-body simulations.
TL;DR: The Birkhoff system is a generalization of the Hamiltonian system and generalized canonical transformations are studied in this paper, where the generalized canonical transformation is extended into the Birkhofian system using the Kailey transformation.
Abstract: The Birkhoff systems are the generalization of the Hamiltonian systems Generalized canonical transformations are studied The symplectic algorithm of the Hamiltonian systems is extended into that of the Birkhoffian systems Symplectic differential scheme of autonomous Birkhoffian systems was structured and discussed by introducing the Kailey Transformation
TL;DR: In this paper, Cervero et al. showed that the classical phase space transformation can be maintained in the operator formalism but the construction of the quantum canonical transformation is not clearly related to the classical generating function of a classical canonical transformation.
Abstract: In this paper we present an approach to quantum mechanical canonical transformations. Our main result is that time-dependent quantum canonical transformations can always be cast in the form of squeezing operators. We revise the main properties of these operators in regard to its Lie group properties, how two of them can be combined to yield another operator of the same class and how can also be decomposed and fragmented. In the second part of the paper we show how this procedure works extremely well for the time-dependent quantum harmonic oscillator. The issue of the systematic construction of quantum canonical transformations is also discussed along the lines of Dirac, Wigner, and Schwinger ideas and to the more recent work by Lee. The main conclusion is that the classical phase space transformation can be maintained in the operator formalism but the construction of the quantum canonical transformation is not clearly related to the classical generating function of a classical canonical transformation. We hereby propose the much more efficient method given by the squeezing operators. This method has also been proved to be very useful, by one of the authors, in the framework of the dynamical symmetries (Cervero, J. M. (1999). International Journal of Theoretical Physics38, 2095–2109).
TL;DR: In this article, the inverse problem for periodic sl(2) lattices is considered as a canonical transformation from the separation to local variables, and a new concept of a factorized separation chain is introduced allowing to solve it explicitly.
Abstract: We consider the inverse problem for periodic sl(2) lattices as a canonical transformation from the separation to local variables. A new concept of a factorized separation chain is introduced allowing to solve the inverse problem explicitly. The method is applied to an arbitrary representation of the corresponding Sklyanin algebra.
TL;DR: In this paper, the relation between the Lagrangian and Hamiltonian BRST symmetry generators for a recently proposed two-dimensional symmetry was analyzed and it was shown that this symmetry may be obtained from a canonical transformation in the ghost sector in a gauge-independent way.
Abstract: We analyze the relation between the Lagrangian and Hamiltonian BRST symmetry generators for a recently proposed two-dimensional symmetry. In particular it is shown that this symmetry may be obtained from a canonical transformation in the ghost sector in a gauge-independent way.
01 Jan 2002
TL;DR: In this article, a canonical transformation is used to relate the Anderson model of localized magnetic moment in a dilute alloy to that of Kondo, and the two models are shown to be equivalent.
Abstract: A canonical transformation is used to relate the Anderson model of a localized magnetic moment in a dilute alloy to that of Kondo. In the limit of small $s\ensuremath{-}d$ mixing, which is the most favorable case for the occurrence of a moment, the two models are shown to be equivalent. The Anderson model thus has low-temperature anomalies similar to those previously discussed for the Kondo model.
TL;DR: In this paper, it was shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the bargainmann transform).
Abstract: This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480–5505 (1995)]—when the configuration space is the two-sphere S2 and for a Bargmann transform that we introduce for the three-sphere S3. It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C3 or C4. We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141–1148 (1977)] and the other qu...
TL;DR: In this article, the origin of this canonical transformation is probed and it is shown that when θ-term appears cosmological, λ-term also appears simultaneously in the gravity without metric formalism of Capovilla, Jacobson and Dell.
Abstract: In the gravity without metric formalism of Capovilla, Jacobson and Dell, the topological θ-term appears through a canonical transformation. The origin of this canonical transformation is probed here. It is shown here that when θ-term appears cosmological, λ-term also appears simultaneously.
TL;DR: An effective Hamiltonian for the two-band Hubbard model was derived by a canonical transformation which was calculated and summed up to infinite order as discussed by the authors, and the transformed Hamiltonian contains terms with strongly renormalized interaction energies.
Abstract: An effective Hamiltonian for the two-band Hubbard model was derived by a canonical transformation which was calculated and summed up to infinite order . The transformed Hamiltonian contains terms with strongly renormalized interaction energies. These new interaction energies show sign reversals as a function of the hopping integral in addition to a strong reduction in the charge-transfer gap and a significant increase in the attractive oxygen Hubbard term.
TL;DR: In this article, a truncated Hamiltonian was proposed for the evolution of cosmological perturbations on superhorizon scales in the case that scalar fields have incommensurable masses.
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TL;DR: In this article, an exact canonical transformation of the energy-time pair to the action-angle canonical pair, $ (E,t) to (I,theta) $, is presented.
Abstract: Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta) $. Quantum mechanical dynamics can be studied in the framework of the new Hamiltonian. This transformation also establishes a relation between a wide class of the energy balance equations and dynamical localization of classical diffusion by quantum interference, that was studied in the field of quantum chaos. An exact solution for a simple system is presented as well.
TL;DR: In this article, the first bound state of two polarons was found by solving an integral equation, which corresponds to a Schrodinger equation describing internal vibrations of a bipolaron, and the Hamiltonian describing these vibrations was separated from the complete Hamiltonian of the electron-phonon system by using the Bogoliubov-Tyablikov method of canonical transformations of coordinates.
Abstract: The ranges of ɛ*/ɛ∞ and of the electron-phonon coupling constant in which the three-dimensional bipolaron exists are determined. The limits of these ranges correspond to the emergence of the first bound state of two polarons. The criteria for the first bound state to arise are found by solving an integral equation, which corresponds to a Schrodinger equation describing internal vibrations of a bipolaron. The Hamiltonian describing these vibrations is separated from the complete Hamiltonian of the electron-phonon system by using the Bogoliubov-Tyablikov method of canonical transformations of coordinates.