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Operator theory

The spectrum of the spin-boson model

Matthias Hübner, Herbert E. Spohn

Published Jan 1, 1994• 3 citations
Publisher

Abstract

Many physical problems can be described as a single (or a few) degrees of freedom interacting with a free field, regarded as a bath or reservoir. It is commonly assumed that a nontrivial coupling to the field serves as a mechanism for the small system to dissipate its energy. This somewhat vague formulation should be made precise by mathematical physics and we take here the point of view that it is reflected in the spectrum of the coupled Hamiltonian. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

DOI
10.1007/978-3-0348-8545-4_29

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The Spectrum of the Spin-Boson Model

Matthias Hübner, Herbert E. Spohn

NATO ASI series. Series B : Physics•Jan 1, 1994•1 citation
Many physical problems can be described as a single (or a few) degrees of freedom interacting with a free field, regarded as a bath or reservoir. It is commonly assumed that a nontrivial coupling to the field serves as a mechanism for the small system to dissipate its energy. This somewhat vague formulation should be made precise by mathematical physics and we take here the point of view that it is reflected in the spectrum of the coupled Hamiltonian. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Classical theories starting with continuous degrees of freedom will typically generate bosonic quantum objects; fermionic quantum objects in turn, arise when a classical system contains discrete degrees of freedom—typically: flip-flops. Here, we explain how anti-commuting operators enter the scene, and illustrate the situation using an elegant model: the idealized notion of a ‘neutrino’. What do neutrinos have in common with infinite, at sheets, and where does spin 12\frac{1}{2}21​ come from? The associated mathematical tool kit is quite delicate. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Even if we still face problems in formulating concise theories that explain the resolution of various apparent paradoxes, one may simply assume such a theory to exist, and that it will one day be found. This leads to the CA (Cellular Automaton) Interpretation. We now formulate the rules. The universe has a wave function, which, in terms of the classical degrees of freedom, collapses continuously, yet fully in agreement with Schrödinger’s equation. We formulate how to look at various notoriously ‘quantum mechanical’ phenomena, such as superposition, exponential decay, and the double slit experiment. What can we say about the ‘quantum computer’? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The conclusion of Part I, the non-technical (or somewhat less technical) part of this book, is that a completely convincing model of our universe is lacking. This should be a model that shows how quantum mechanical behaviour, with all its mysteries and paradoxes, can emerge from a local, deterministic theory. Yet we also find that one can assume its existence to arrive at a picture of our quantum mechanical universe that makes perfect sense. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.