Universal Dynamical Control of Quantum Mechanical Decay: Modulation of the Coupling to the Continuum

AbstractThe quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated. The Coulomb propagator generally consists of two parts. The sum of the discrete part of the spectrum is extrapolated numerically, while three integration procedures are applied to the continuum part of the oscillating integral: the Gauss–Pollaczek quadrature, the Gauss–Legendre quadrature along the real axis, and a transformation into a contour integral in the complex plane with the subsequent Gauss–Legendre quadrature. Using the contour integral, the Coulomb propagator can be calculated very accurately from an L$$^2$$ 2 basis. Using the three-term recursion relation of the Pollaczek polynomials, an effective algorithm is herein presented to reduce the number of integrations. Numerical results are presented and discussed for all procedures.

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Universal dynamical control of decay and decoherence for weak and strong system-bath coupling

Quantum Information and Computation ◽

10.26421/qic5.45-3 ◽

2005 ◽

Vol 5 (4&5) ◽

pp. 285-317

Author(s):

G. Gordon ◽

G. Kurizki ◽

A.G. Kofman ◽

S. Pellegrin

Keyword(s):

Random Phase ◽

Quantum Systems ◽

Unified Theory ◽

Phase Fluctuations ◽

Strongly Coupled ◽

Weakly Coupled ◽

Abrupt Changes ◽

Dynamical Control ◽

Strong System ◽

The Continuum

A unified theory is given of dynamically modified decay and decoherence in driven two-level and multilevel quantum systems that are weakly coupled to arbitrary finite-temperature reservoirs and undergo random phase fluctuations. Criteria for the optimization of decoherence suppression and the limitations of this approach are obtained. For a driven qubit that is strongly coupled to the continuum edge of reservoir's spectrum, we demonstrate that only an appropriately ordered sequence of abrupt changes of the resonance frequency, near the continuum edge, can effectively protect the qubit state from decoherence.

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Continuum models and Morse Theory in the simulation, design and evaluation of magnetic Skyrmion devices

10.36227/techrxiv.15062844 ◽

2021 ◽

Author(s):

P. Robert Kotiuga

Keyword(s):

Morse Theory ◽

Lattice Models ◽

Energy Functional ◽

Continuum Models ◽

Quantum Mechanical ◽

Simulation Design ◽

Lattice Systems ◽

Solid Foundation ◽

Magnetic Skyrmions ◽

The Continuum

Nanomagnetic devices such as computer gates and memory devices based on magnetic skyrmions are close to becoming a reality. In this paper we will explore the highly nonconvex nanomagnetic energy landscape in order to draw conclusions about the complexity of magnetic phenomena. Morse theoretic arguments show that, in a bounded energy interval, the number of critical points of the energy functional grows exponentially. To show this, we introduce a hierarchy of models for the design of nanomagnetic devices to provide a solid foundation for the introduction of topological tools. To reason in terms of lattice models, one must make a distinction between two types of lattices: the quantum mechanical model of the actual physical lattice and the lattice model that can be associated with a discretization of a continuum model of the physics. By focusing on the implications of Morse theory applied to lattice systems arising from the discretization of the continuum models, and the notion of “topological frustration”, we provide a framework for understanding “complexity” in the context of nanomagnetic systems. We conclude with some suggestions for making the analysis more qualitative.

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Continuum models and Morse Theory in the simulation, design and evaluation of magnetic Skyrmion devices

10.36227/techrxiv.15062844.v1 ◽

2021 ◽

Author(s):

P. Robert Kotiuga

Keyword(s):

Morse Theory ◽

Lattice Models ◽

Energy Functional ◽

Continuum Models ◽

Quantum Mechanical ◽

Simulation Design ◽

Lattice Systems ◽

Solid Foundation ◽

Magnetic Skyrmions ◽

The Continuum

Nanomagnetic devices such as computer gates and memory devices based on magnetic skyrmions are close to becoming a reality. In this paper we will explore the highly nonconvex nanomagnetic energy landscape in order to draw conclusions about the complexity of magnetic phenomena. Morse theoretic arguments show that, in a bounded energy interval, the number of critical points of the energy functional grows exponentially. To show this, we introduce a hierarchy of models for the design of nanomagnetic devices to provide a solid foundation for the introduction of topological tools. To reason in terms of lattice models, one must make a distinction between two types of lattices: the quantum mechanical model of the actual physical lattice and the lattice model that can be associated with a discretization of a continuum model of the physics. By focusing on the implications of Morse theory applied to lattice systems arising from the discretization of the continuum models, and the notion of “topological frustration”, we provide a framework for understanding “complexity” in the context of nanomagnetic systems. We conclude with some suggestions for making the analysis more qualitative.

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Bound states in the continuum in asymmetrical quantum-mechanical and electromagnetic waveguides

Physical Review B ◽

10.1103/physrevb.104.125414 ◽

2021 ◽

Vol 104 (12) ◽

Author(s):

N. M. Shubin ◽

A. V. Friman ◽

V. V. Kapaev ◽

A. A. Gorbatsevich

Keyword(s):

Bound States ◽

Quantum Mechanical ◽

The Continuum

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THE BERRY PHASE AND MONOPOLES IN NON-ABELIAN GAUGE THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x02005840 ◽

2002 ◽

Vol 17 (02) ◽

pp. 157-174 ◽

Cited By ~ 8

Author(s):

F. V. GUBAREV ◽

V. I. ZAKHAROV

Keyword(s):

Gauge Theory ◽

Wilson Loop ◽

Continuum Limit ◽

Gauge Theories ◽

Berry Phase ◽

Quantum Mechanical ◽

Abelian Gauge ◽

Dynamical Phase ◽

Physical Consequences ◽

The Continuum

We consider the quantum mechanical notion of the geometrical (Berry) phase in SU(2) gauge theory, both in the continuum and on the lattice. It is shown that in the coherent state basis eigenvalues of the Wilson loop operator naturally decompose into the geometrical and dynamical phase factors. Moreover, for each Wilson loop there is a unique choice of U(1) gauge rotations which do not change the value of the Berry phase. Determining this U(1) locally in terms of infinitesimal Wilson loops we define monopole-like defects and study their properties in numerical simulations on the lattice. The construction is gauge dependent, as is common for all known definitions of monopoles. We argue that for physical applications the use of the Lorentz gauge is most appropriate. And, indeed, the constructed monopoles have the correct continuum limit in this gauge. Physical consequences are briefly discussed.

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Theory of Dissociative Ionization Processes

Laser Chemistry ◽

10.1155/lc.3.73 ◽

1983 ◽

Vol 3 (1-6) ◽

pp. 73-83 ◽

Cited By ~ 2

Author(s):

S. Kanfer ◽

M. Shapiro

Keyword(s):

Body Wave ◽

Inelastic Collisions ◽

Quantum Mechanical ◽

Penning Ionization ◽

Continuum States ◽

Coupled Channels ◽

Quantum Mechanical Theory ◽

Artificial Channel ◽

Three Body ◽

The Continuum

A quantum mechanical theory for the ℏω+AB→A+B++e- three body breakup is presented. The theory is based on the Continuum Coupled Channels expansion (CCC) in which the three body wave-function is expanded in terms of square integrable and (flux carrying) continuum states. The theory consistently treats the accompanying processes of three body inelastic collisions, dissociative attachment and Penning ionization. Applications to the dissociative photoionization of H2 and HD are presented. The relevant equations are solved exactly using the Artificial Channel method. Excellent agreement is obtained with experiment, concerning the proton kinetic energy distribution.

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The importance of basis states: an example using the hydrogen basis

Canadian Journal of Physics ◽

10.1139/cjp-2014-0726 ◽

2015 ◽

Vol 93 (10) ◽

pp. 1009-1014

Author(s):

Lindsay Forestell ◽

Frank Marsiglio

Keyword(s):

Simple System ◽

Basis Set ◽

Quantum Mechanical ◽

Hamiltonian Matrix ◽

Electron Configuration ◽

Continuum States ◽

Complete Basis ◽

Quantum Mechanical Description ◽

Complete Basis Set ◽

The Continuum

We use a simple system, the electron configuration in a hydrogen-like atom, to demonstrate the importance of using a complete basis set to provide a proper quantum mechanical description. We first start with what may be considered a successful strategy — to diagonalize a truncated Hamiltonian matrix, written in a basis consisting of hydrogen (Z = 1) basis states. This fails to provide the correct answer, and we then demonstrate that the continuum basis states provided the rest of the true wave function, for the bound ground states. This work then shows, in a relatively simple system, the need to utilize a complete basis set, consisting of both bound and continuum states.

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