scholarly journals ACTION WITH ACCELERATION I: EUCLIDEAN HAMILTONIAN AND PATH INTEGRAL

2013 ◽  
Vol 28 (27) ◽  
pp. 1350137 ◽  
Author(s):  
BELAL E. BAAQUIE
Keyword(s):  
Boundary Conditions ◽  
Path Integral ◽  
Degrees Of Freedom ◽  
Similarity Transformation ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Quantum Mechanical System ◽  
The Matrix ◽  
Correct Boundary Conditions ◽  
Acceleration Term

An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.

scholarly journals Über der Kopplung von Schwingungsfreiheitsgraden an die Koordinate intramolekularer Umlagerungen / Coupling of Vibrational Degrees of Freedom lo the Coordinate of Intramolecular Rearrangements

1973 ◽  
Vol 28 (11) ◽  
pp. 1759-1781 ◽  
Author(s):  
J. Brickmann
Keyword(s):  
Degrees Of Freedom ◽  
Energy Surface ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Damping Term ◽  
Intramolecular Rearrangements ◽  
Quantum Numbers ◽  
The Matrix ◽  
Localized Quantum States ◽  
Internal Degrees Of Freedom

Intramolecular rearrangements A ⇌ B are investigated, which can be described in terms of the motion of an effective quantum mechanical ‘‘particle’’ on an energy surface with at least two minima. We regard the energy surface as a function of a limited number of relevant internal degrees of freedom. The rate of isomerization is calculated from the matrix elements of a transition operator W with respect to the localized quantum states of the two isomers, and the coupling to the inter- and intramolecular degrees of freedom, not explizitely considered in the energy surface. It is shown that the matrixelements of W be reduced to integrals over functions of the adiabatic reaction coordinate of the isomerization, and selection rules for the vibrational quantum numbers for the motion perpendicular to this coordinate. The degrees of freedom not relevant for the reaction are summarily taken into account by introducing a heath bath in thermodynamic equilibrium and a simple damping term. Applications are discussed.

scholarly journals Matrix models and deformations of JT gravity

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200582
Author(s):  
Edward Witten
Keyword(s):  
Matrix Models ◽  
Path Integral ◽  
Matrix Model ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Quantum Mechanical System ◽  
Specific Procedure ◽  
Dimensional Theory ◽  
Specific Quantum

Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action − 1 / 2 ∫ d 2 x g ϕ ( R + 2 ) , is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action − 1 / 2 ∫ d 2 x g ( ϕ R + W ( ϕ ) ) is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if W (0) = 0, and otherwise a rather complicated answer.

A Spherical DC Servo Motor With Three Degrees of Freedom

1989 ◽  
Vol 111 (3) ◽  
pp. 398-402 ◽  
Author(s):  
K. Kaneko ◽  
I. Yamada ◽  
K. Itao
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Matrix Elements ◽  
Servo Motor ◽  
Constant Matrix ◽  
Spherical Motor ◽  
The Matrix ◽  
Three Degrees Of Freedom

A spherical DC servo motor with three degrees of freedom is proposed. First, the process of generating three-dimensional torque is analyzed to obtain the torque constant matrix. The matrix elements are shown to vary with rotor inclination, and winding currents are shown to interfere with each other. Then, the dynamics of the spherical motor are investigated theoretically and experimentally, considering torque interference, gyro moment and gravity. Finally, the trajectory of the prototype motor is shown in order to clarify its abilities. This new spherical motor is expected to produce a smaller, a lighter mechanism, since no gears or linkages are needed.

RADIATIVE EFFECTS IN A CONSTANT MAGNETIC FIELD USING THE QUANTUM MECHANICAL PATH-INTEGRAL

1994 ◽  
Vol 09 (23) ◽  
pp. 2167-2178 ◽  
Author(s):  
D.G.C. MCKEON ◽  
T.N. SHERRY
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Path Integral ◽  
Constant Magnetic Field ◽  
Quantum Mechanical ◽  
Quantum Field ◽  
Matrix Elements ◽  
Loop Momentum ◽  
Background Magnetic Field

It has been shown how evaluation of matrix elements of the form <x| exp −iHt|y> using the quantum mechanical path-integral allows one to determine radiative corrections in quantum field theory without encountering loop momentum integrals. In this paper we show how this technique can be applied when there is a constant background magnetic field contributing to the “Hamiltonian” H.

Path integral on non-simply connected space and problem with zero boundary condition

1992 ◽  
Vol 70 (5) ◽  
pp. 375-378
Author(s):  
Hoang Ngoc Long
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Path Integral ◽  
Evolution Operator ◽  
Finite Interval ◽  
Path Integrals ◽  
Matrix Elements ◽  
Path Integral Formulation ◽  
Connected Space ◽  
Simply Connected

In this paper a path integral formulation for various matrix elements of the evolution operator in a finite interval with zero boundary conditions is presented. Connection of these matrix elements with path integrals on a non-simply-connected space is given as well.

Vacuum polarization in a background magnetic field in (2 + 1)-dimensional QED

1995 ◽  
Vol 73 (7-8) ◽  
pp. 458-462
Author(s):  
D. G. C. McKeon
Keyword(s):  
Magnetic Field ◽  
Path Integral ◽  
Vacuum Polarization ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Integral Technique ◽  
Background Magnetic Field ◽  
The One

The one-loop vacuum polarization in the presence of a background magnetic field is computed in (2 + 1)-dimensional electrodynamics in which the spinor mass is parity violating. The quantum-mechanical path-integral technique is used to compute matrix elements arising in the context operator regularization.

scholarly journals On quantum-mechanical equations of motion in representation dependent of external sources

2017 ◽  
Vol 32 (32) ◽  
pp. 1750189
Author(s):  
Igor A. Batalin ◽  
Peter M. Lavrov
Keyword(s):  
Normal Form ◽  
Boundary Conditions ◽  
Path Integral ◽  
Equations Of Motion ◽  
Quantum Mechanical ◽  
Motion Equations ◽  
Closed Solution ◽  
Boundary Terms ◽  
External Sources

In the present paper, we consider in detail the aspects of the Heisenberg’s equations of motion, related to their transformation to the representation dependent of external sources. We provide with a closed solution as to the variation-derivative motion equations in the general case of a normal form (symbol) chosen. We show that the action in the path integral does depend actually on a particular choice of a normal symbol. We have determined both the aspects of the latter dependence: the specific boundary conditions for virtual trajectories, and the specific boundary terms in the action.

scholarly journals MATRIX QUANTIZATION OF TURBULENCE

2012 ◽  
Vol 22 (09) ◽  
pp. 1250213 ◽  
Author(s):  
EMMANUEL FLORATOS
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Evolution Equations ◽  
Lorenz System ◽  
Quantum Mechanical ◽  
Noncommutative Phase Space ◽  
Commutation Relations ◽  
The Matrix ◽  
Lorenz Attractors ◽  
Volume Preserving

Based on our recent work on Quantum Nambu Mechanics [Axenides & Floratos 2009], we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of noncommutative phase space coordinates as Hermitian N × N matrices in R3. For the volume preserving part, they satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction, it violates the quantum commutation relations. We demonstrate that the Heisenberg–Nambu evolution equations for the Matrix Lorenz system develop fast decoherence to N independent Lorenz attractors. On the other hand, there is a weak dissipation regime, where the quantum mechanical properties of the volume preserving nondissipative sector survive for long times.

scholarly journals Boundary dynamics and topology change in quantum mechanics

2015 ◽  
Vol 12 (08) ◽  
pp. 1560011 ◽  
Author(s):  
J. M. Pérez-Pardo ◽  
M. Barbero-Liñán ◽  
A. Ibort
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Necessary Conditions ◽  
Quantum Systems ◽  
Quantum Mechanical ◽  
Manifolds With Boundary ◽  
Quantum Mechanical System ◽  
Topology Change ◽  
And Topology ◽  
Boundary Dynamics

We show how to use boundary conditions to drive the evolution on a quantum mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schrödinger equation. In particular, we will need the theory of self-adjoint extensions of differential operators in manifolds with boundary. An introduction of the latter as well as meaningful examples will be given. It is known that different boundary conditions can be used to describe different topologies of the associated quantum systems. We will use the previous results to study the topology change and to obtain necessary conditions to accomplish it in a dynamical way.

scholarly journals Решение обратной задачи для сложного вибронного аналога резонанса Ферми на основе плоских вращений Якоби

2020 ◽  
Vol 128 (11) ◽  
pp. 1614
Author(s):  
В.А. Кузьмицкий
Keyword(s):  
Eigenvalue Problem ◽  
Spectral Data ◽  
Similarity Transformation ◽  
Accurate Solution ◽  
Fermi Resonance ◽  
Matrix Elements ◽  
Second Stage ◽  
The Matrix ◽  
Two Stages ◽  
Orthogonal Similarity Transformation

Based on algebraic methods, we have found an accurate solution for the inverse task for the vibronic analogue of the complex Fermi resonance, i.e. the determination from the spectral data (energies Ek and transition intensities Ik of the observed conglomerate of lines, k = 1, 2, ..., n; n > 2) energies of the «dark» states Am and the matrix elements of their coupling Bm with the «bright» state. The algorithm consists of two stages. At the first stage, the Jacobi plane rotations are used to construct an orthogonal similarity transformation matrix X, for which the elements of the first row obey the requirement (X1k)^2 = Ik, which corresponds to that fact that there is only one non-perturbed «bright» state. At the second stage, the quantities Am and Bm are obtained after solving the eigenvalue problem for block of «dark» states of the matrix Xdiag({Ek})X-1.

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