Showing papers on "Open quantum system published in 1969"
[...]
TL;DR: The Hamiltonian methods of Arnowitt, Deser, and Misner can be applied to homogeneous cosmological models, and prove to be an efficient way both of constructing the Einstein equations and of studying their solutions as mentioned in this paper.
Abstract: The Hamiltonian methods of Arnowitt, Deser, and Misner can be applied to homogeneous cosmological models, and prove to be an efficient way both of constructing the Einstein equations and of studying their solutions. By using an appropriate form for the metric, one finds that the constraint equations for these models can be solved explicitly, and the resulting problem in Hamiltonian mechanics resembles that of a particle in a potential well. The most unusual feature of the Hamiltonian is that it is explicitly time dependent. There is an easy and attractive choice of factor orderings which allows one to pass on to a quantum theory (by imposing canonical commutation relations on the independent canonical variables) while maintaining the signature of the quantized metric. For the closed-space cosmological model (Bianchi type IX) which is studied in most detail, a classical (high-quantum-number) state remains classical as the wave function is followed back in time toward the initial singularity. There is no tendency for significant contributions from states of low quantum number to develop even when the radius of the universe is much less than ${(\frac{G\ensuremath{\hbar}}{{c}^{3}})}^{\frac{1}{2}}={10}^{\ensuremath{-}33}$ cm.
451 citations
Book•
01 Jan 1969
TL;DR: In this paper, the authors propose a new model for quantum computing which has attracted a lot of attention, especially from Microsoft inc. (Freedman 1998), is the Topological-Quantum-Field-Theory (TQFT) algorithm.
Abstract: Quantum Mechanics Made Simple: Lecture NotesQuantum Field Theory and the Standard Model: Schwartz Learn quantum computing: a field guide IBM QuantumQuantum Field TheoryIntroduction to Classical Field TheoryQuantum Field Theory and Standard ModelJohn Preskill theory.caltech.eduNonlocality and Entanglement Quantum Theory and the Lecture Notes on Quantum Field Theory Kevin ZhouSolutions to Problems in Quantum Field TheoryDavid Tong: Lectures on Quantum Field TheoryIntroduction to Quantum Field TheoryRelativistic Quantum Field Theory I | Physics | MIT Quantum field theory WikipediaQuantum Computing (Stanford Encyclopedia of Philosophy)An Introduction To Quantum Field Theory | Michael E Quantum Field theory vs. many-body Quantum Mechanics Introduction to Quantum Field TheoryAn Introduction to String TheoryCan We Gauge Quantum Time of Flight? Scientific AmericanIntroduction to quantum mechanics WikipediaQuantum Field Theory (Stanford Encyclopedia of Philosophy)David Tong: Quantum Field TheoryQuantum Field Theory DAMTPQuantum Theory an overview | ScienceDirect TopicsAn Introduction to Quantum Computing Dec 03, 2006 · 3.4 Topological-Quantum-Field-Theory (TQFT) Algorithms. Another exotic model for quantum computing which has attracted a lot of attention, especially from Microsoft inc. (Freedman 1998), is the
427 citations
TL;DR: In this paper, the authors introduce the concept of quantum stochastic process, where observations of the arrival of quanta at a counter are made throughout an interval of time, and describe rigorously certain measurement procedures.
Abstract: In order to describe rigorously certain measurement procedures, where observations of the arrival of quanta at a counter are made throughout an interval of time, it is necessary to introduce the concept of a quantum stochastic process. While fully quantum mechanical in nature, these have a great deal of similarity with classical stochastic processes and can be characterized by and constructed from their infinitesimal generators. The infinitestimal generators are naturally obtained from certain “fields” which we prove must be of the boson or fermion type.
231 citations
220 citations
TL;DR: In this article, the modular variable is introduced to bring out the physical features of quantum mechanical non-locality, such as the quantum effects of electromagnetic potentials, which is particularly conspicuous in quantum phenomena without a classical analog.
Abstract: The non-local aspects of interaction between quantum systems are investigated. These aspects are particularly conspicuous in quantum phenomena without a classical analog, such as the quantum effects of electromagnetic potentials. The study of the potential effect leads to the introduction of a new type of dynamical variable, the modular variable, which brings out the physical features of quantum mechanical non-locality.
139 citations
TL;DR: A remarkable feature of the 1968 conference of Nobel prize winners in physics at Lindau is that it was possible for me to ask such a question in the presence of two of the founders of quantum mechanics, Werner Heisenberg and P.M. Dirac, more than 30 years after the discovery, in a lecture attended by 400 students who had recently begun their study of the subject as discussed by the authors.
Abstract: WHAT IS QUANTUM MECHANICS? A remarkable feature of the 1968 conference of Nobel prize winners in physics at Lindau is that it was possible for me to ask such a question in the presence of two of the founders of quantum mechanics, Werner Heisenberg and P.A.M. Dirac, more than 30 years after the discovery, in a lecture attended by 400 students who had recently begun their study of the subject. Several answers to the question are possible. The only easy one is that quantum mechanics is a discipline that provides a wonderful set of rules for calculating physical properties of matter. For such simple systems as hydrogen and helium atoms the calculated energy levels agree with experiment to fantastic accuracy. In more complicated cases the computations are difficult and the accuracy is lower, but it is reasonable to believe, in principle at least, that the theory would be adequate if only the calculational problems could be overcome.
119 citations
TL;DR: In this paper, the Hermitean operators F = A*A represent quantum effects as defined axiomatically byLudwig and are discussed under the assumption that they are caused by interactions with another system (apparatus), described by aS matrix.
Abstract: States of a quantum system may be influenced by an external intervention. FollowingHaag andKastler, such a transformation of states is called an operation, and is called pure if it transforms pure states into pure states. Operations are discussed here under the assumption that they are caused by interactions with another system (apparatus), described by aS matrix. Pure operations are then shown to correspond, with one exception, to operatorsA with norm smaller than one. The Hermitean operatorsF=A*A represent quantum effects as defined axiomatically byLudwig. The particular case of local operations in quantum field theory is also investigated.
118 citations
TL;DR: In this paper, it was shown that the spontaneous transitions of atoms can be solved without the need for field quantisation, provided the universe is a perfect absorber along the future light cone and the usual formulae for level shifts and spontaneous transitions can be obtained in a steady-state model of the universe.
75 citations
TL;DR: In this article, the authors put algebraic quantum theory into the context of a probabilistic interpretation with emphasis on local measurements, and examined certain general features of the theory and proved the connexion with Wigner's Theorem.
Abstract: After briefly putting algebraic quantum theory into the context of a probabilistic interpretation with emphasis on local measurements, certain general features of the theory are examined. Sectors are defined and shown to be the components of the pure state space in the norm topology. Transition probabilities are defined by a simple algebraic formula and it is shown how superpositions of pure states may be defined. With the aid of these results, symmetries are characterized and the connexion with Wigner's Theorem is established.
57 citations
TL;DR: In this paper, a self-adjoint extension of a C*-automorphism group for positive-energy symmetric (or "Bose-Einstein") quantum fields is presented.
Abstract: 1. This note treats the C*-dynamics of positive-energy symmetric (or 'Bose-Einstein') quantum fields in continuation of [ l ] . The temporal development of the systems being considered is given by a one-parameter group of automorphisms of a C*-algebra, which in general are not unitarily implemented, but may by a process of localization be reduced to the consideration of a complex of putative one-parameter unitary groups. Each such group is to be generated by an operator H' which is formally given as H+ V, where each of H and V may be formulated as a selfadjoint operator in Hubert space, but whose sum is a priori ill-defined as such because of the singular nature of V in relation to H. In [l , I ] a theory of renormalized products of quantum fields was initiated which served as a basis for the treatment of the operators V of concrete interest. I t followed that for a certain class of relativistic cases: (a) H+V is densely defined and has a selfadjoint extension H'\ (b) the associated complex of one-parameter unitary groups corresponds to a C*-automorphism group provided the Lie formula: e' =limn(e e) is applicable (as is the case e.g. if H' is unique, by a theorem of Trotter). In the present note, by making a natural use of mild particularities of the operators in question, a selfadjoint extension H' is constructed which has the modified property, sufficient for the construction of an appropriate C*-automorphism group, that e' = limmlimn(e e), if {fm} is any sequence of real functions of compact support on R such that/m(X)—>X and |/m(X)| ^ | X | ; and this operator has in addition many other relevant properties. The treatment is quite general, and apart from the finiteness of the moments of V and e~, and the nonvanishing of the 'mass/ makes no significant assumptions.
TL;DR: In this article, the confusion about the exact form of the rotation operators in quantum mechanics is cleared up by indicating some well hidden errors in the two standard books on angular momentum, which are used in this paper.
TL;DR: In this paper, an interpretation of the process of measurement is proposed which can be placed wholly within the quantum theory, and the entire system including the apparatus and even the mind of the observer can be considered to develop according to the Schrodinger equation.
Abstract: An interpretation of the process of measurement is proposed which can be placed wholly within the quantum theory. The entire system including the apparatus and even the mind of the observer can be considered to develop according to the Schrodinger equation. No separation, in principle, of the observer and the observed is necessary; nor is it necessary to introduce either the type I process of von Neumann or wave function reduction.
TL;DR: In all representations of the canonical commutation relations, there is a common, invariant domain of essential self-adjointness for quantum fields and conjugate momenta as mentioned in this paper.
Abstract: In all representations of the canonical commutation relations, there is a common, invariant domain of essential self-adjointness for quantum fields and conjugate momenta.
TL;DR: In this article, it is shown that in ordinary quantum mechanics the formal definition of coexistence and the corresponding postulates given by Ludwig are consistent with the dynamics of interaction processes leading to effects.
Abstract: Effects are defined in this paper as observable changes in the state of a macrosystem, which are caused by interaction with a microsystem. These effects are the starting point of Ludwig's axiomatic foundation of quantum theory. In this theory the concept of commensurability is developed by considering effects which can be caused together, by one single microsystem. Such effects are called coexistent. It is shown that in ordinary quantum mechanics the formal definition of coexistence and the corresponding postulates given by Ludwig are consistent with the dynamics of interaction processes leading to effects.
TL;DR: A quantum logic structure for quantum mechanics which contains the concepts of a physical space, localizability, and symmetry groups is formulated in this paper, and it is shown that there is an underlying Hilbert space which mirrors much of this axiomatic structure.
Abstract: A quantum logic structure for quantum mechanics which contains the concepts of a physical space, localizability, and symmetry groups is formulated. It is shown that there is an underlying Hilbert space which mirrors much of this axiomatic structure. Quantum fields are defined and shown to arise naturally from the quantum logic structure. The fields ofHaag andWightman are generalized to this theory and an attempt is made to find a local equivalence for these fields.
TL;DR: In this article, a Lorentz-invariant description of quantum scattering processes of tachyons is given, and the pole structure of the connected part of the scattering amplitude is derived.
Abstract: A Lorentz-invariant description of quantum scattering processes of tachyons is given. Space-time considerations are used to derive the pole structure of the connected part of the scattering amplitude.
TL;DR: In this paper, the authors describe an extension of the theory of these basic functions (or ''renormalized products of quantum fields'' to general space-times and laws of dependence of the energy on the momentum, relativistic theory in a Minkowski space of any dimension being a rather special case.
Abstract: 1. In earlier work [ l ] , [2], the generalized nonlinear functions which enter formally into certain nonlinear relativistic quantized partial differential equations in a two-dimensional space-time were given mathematical formulation and treatment. The theory of these highly singular functions, and in particular their locality, when combined with hyperbolicity ideas implemented by the use of the Lie-Trotter formula, gave a means of adapting the treatment of quantum field dynamics in terms of a group of automorphisms of a C*-algebra, developed initially in [3], to the equations in question. The present work describes an extension of the theory of these basic functions (or \"renormalized products of quantum fields\")» to general space-times and laws of dependence of the energy on the momentum, relativistic theory in a Minkowski space of any dimension being a rather special case. The general dynamical implications of these results will be treated later.
TL;DR: In this paper, it was shown that α-particle emission contradicts the usual interpretation of quantum mechanics, but is in agreement with the first guided particle model proposed by Bohm.
01 Jan 1969
TL;DR: In this paper, it was shown that the point spectrum of internal symmetries is always symmetric, provided the intersection of all local subalgebras is trivial, and it is shown that internal symmetric point spectrum is a group of classes of symmetric points.
Abstract: It is shown that the point spectrum of internal symmetries is always symmetric. It is a group provided the intersection of all local subalgebras is trivial.