Effective Hamiltonians for Constrained Quantum Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Effective Hamiltonians for Constrained Quantum Systems write by Jakob Wachsmuth. This book was released on 2014-06-05. Effective Hamiltonians for Constrained Quantum Systems available in PDF, EPUB and Kindle. The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.
Effective Hamiltonians for Constrained Quantum Systems
Effective Hamiltonians for Constrained Quantum Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Effective Hamiltonians for Constrained Quantum Systems write by Jakob Wachsmuth. This book was released on 2014-10-03. Effective Hamiltonians for Constrained Quantum Systems available in PDF, EPUB and Kindle. The authors consider the time-dependent Schrodinger equation on a Riemannian manifold $\mathcal{A}$ with a potential that localizes a certain subspace of states close to a fixed submanifold $\mathcal{C}$. When the authors scale the potential in the directions normal to $\mathcal{C}$ by a parameter $\varepsilon\ll 1$ the solutions concentrate in an $\varepsilon$-neighborhood of $\mathcal{C}$. This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrodinger equation on the submanifold $\mathcal{C}$ and show that its solutions suitably lifted to $\mathcal{A}$ approximate the solutions of the original equation on $\mathcal{A}$ up to errors of order $\varepsilon DEGREES3t$ at time $t$. Furthermore the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order $\varepsilon DEGREES3$ with those of the full Hamiltonian under reasonab
Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem
Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem write by Jonah Blasiak. This book was released on 2015-04-09. Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem available in PDF, EPUB and Kindle. The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.
Local Entropy Theory of a Random Dynamical System
Local Entropy Theory of a Random Dynamical System - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Local Entropy Theory of a Random Dynamical System write by Anthony H. Dooley. This book was released on 2014-12-20. Local Entropy Theory of a Random Dynamical System available in PDF, EPUB and Kindle. In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk
Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk write by A. Rod Gover. This book was released on 2015-04-09. Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk available in PDF, EPUB and Kindle. The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.
