Search results for "Configuration space"
showing 10 items of 32 documents
Inherent structure entropy of supercooled liquids
1999
We present a quantitative description of the thermodynamics in a supercooled binary Lennard Jones liquid via the evaluation of the degeneracy of the inherent structures, i.e. of the number of potential energy basins in configuration space. We find that for supercooled states, the contribution of the inherent structures to the free energy of the liquid almost completely decouples from the vibrational contribution. An important byproduct of the presented analysis is the determination of the Kauzmann temperature for the studied system. The resulting quantitative picture of the thermodynamics of the inherent structures offers new suggestions for the description of equilibrium and out-of-equilib…
Classical Geometric Phases: Foucault and Euler
2020
In the last chapter we saw how a quantum system can give rise to a Berry phase, by studying the adiabatic round trip of its quantum state on a certain parameter space. Rather than considering what happens to states in Hilbert space, we now turn to classical mechanics, where we are concerned instead with the evolution of the system in configuration space. As a first example, we are interested in the geometric phase of an oscillator that is constrained to a plane that is transported over some surface which moves along a certain path in three-dimensional space. Contrary to determining the Berry phase, there is no adiabatic approximation of the motion along the curve involved. The Foucault phas…
A new approach to interacting fields
1974
A model for a description of interaction, which involves particle creation, can be given as follows: (1) A smooth finite-dimensional manifoldM constitutes the configuration space of some interacting system. (2) The concept of an interacting field is formulated in terms of two-component objects which consist of a physical and a topological field component which are ‘derived’ fromM. (3) Interaction is described in terms of the topological linking number of the topological field components and in terms of the intrinsic field equations.
The Action Principles in Mechanics
2001
We begin this chapter with the definition of the action functional as time integral over the Lagrangian \(L(q_{i}(t),\dot{q}_{i}(t);t)\) of a dynamical system: $$\displaystyle{ S\left \{[q_{i}(t)];t_{1},t_{2}\right \} =\int _{ t_{1}}^{t_{2} }dt\,L(q_{i}(t),\dot{q}_{i}(t);t)\;. }$$
CQ*-Algebras of Operators and Application to Quantum Models
2000
C*-algebras constitute, as known, the cornerstones of the Haag-Kastler [1] algebraic approach to quantum systems, with infinitely many degrees of freedom: one usually starts, in fact, with associating to each bounded region V of the configuration space of the system the C*-algebra A v of local observables in V. The uniform completion A of the algebra A0 generated by the Av’s is then considered as the C*-algebra of observables of the system.
Coordinates for quasi-Fuchsian punctured torus space
1998
We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely the classical Fuchsian space with Fenchel-Nielsen coordinates and the Maskit embedding. We also show how they relate to the pleating coordinates of Keen and Series.
Calculating loops without loop calculations: Next-to-leading order computation of pentaquark correlators
2012
We compute next-to-leading order (NLO) perturbative QCD corrections to the correlators of interpolating pentaquark currents and their absorptive parts. We employ modular techniques in configuration space which saves us from the onus of having to do loop calculations. The modular technique is explained in some detail. We present explicit NLO results for several interpolating pentaquark currents that have been written down in the literature. Our modular approach is easily adapted to the case of NLO corrections to multiquark correlators with an arbitrary number of quarks/antiquarks.
Closed form for two-photon free–free transition matrix elements
2000
Abstract Two-photon free–free transitions happen in the multiphoton ionization with more than one excess photon and in bremsstralung. Up to now, the configuration space free–free transition amplitudes have not been written in closed form. We propose a modified Coulomb Green’s function (CGF) Sturmian expansion which allows one to obtain expressions for two-photon radial transition matrix elements in the closed form which are easy to continue analytically to calculate free–free transitions in H.
Non-Equilibrium Markov State Modeling of the Globule-Stretch Transition
2016
We describe a systematic approach to construct coarse-grained Markov state models from molecular dynamics data of systems driven into a nonequilibrium steady state. We apply this method to study the globule-stretch transition of a single tethered model polymer in shear flow. The folding and unfolding rates of the coarse-grained model agree with the original detailed model. We demonstrate that the folding and unfolding proceeds through the same narrow region of configuration space but along different cycles.
Some results on the rotated infinitely deep potential and its coherent states
2021
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, he…