Showing papers on "Open quantum system published in 1974"
TL;DR: In this article, the time dependence of ρ11, ρ22 and ρ12 under steady-state conditions was analyzed under a light field interaction V = -μ12Ee iωt + c.c.
Abstract: (b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>
1,872 citations
Book•
01 Jan 1974
TL;DR: In this article, a phenomenological theory of magnetic order impurities and alloys external fields electrons, phonons, and transport aspects of the electron-electron interaction is presented.
Abstract: Electronic structure lattice dynamics symmetry and its consequences phenomenological theories of magnetic order impurities and alloys external fields electrons, phonons, and transport aspects of the electron-electron interaction.
832 citations
TL;DR: For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx-andp-space around −1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space.
Abstract: For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space aroundħ−1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,ħ−1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.
608 citations
Book•
01 Jan 1974
342 citations
TL;DR: In this article, a convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space, and the physical interpretation of the scheme is given in terms of generalized impossibility principles.
Abstract: A convex scheme of quantum theory is outlined where the states are not necessarily the density matrices in a Hilbert space. The physical interpretation of the scheme is given in terms of generalized “impossibility principles”. The geometry of the convex set of all pure and mixed states (called a statistical figure) is conditioned by the dynamics of the system. This provides a method of constructing the statistical figures for non-linear variants of quantum mechanics where the superposition principle is no longer valid. Examples of that construction are given and its possible significance for the interrelation between quantum theory and general relativity is discussed.
246 citations
136 citations
TL;DR: In this paper, the formalism of covariant conditional expectations is described as leading to an operational definition of generalized observables in quantum mechanics, wide enough to account for the fuzziness inherent in actual measurement processes, relative to a multidimensional physical continuum.
Abstract: The formalism of covariant conditional expectations is described as leading to an operational definition of generalized observables in quantum mechanics, wide enough to account for the fuzziness inherent in actual measurement processes, relative to a multidimensional physical continuum. As an application, a position operator for the photon is defined and its intrinsic fuzziness is discussed.
113 citations
TL;DR: In this paper, a review of the attempts to obtain a quantum theory of gravitation is presented, and the essential ideas of those programmes on which extensive work has been done are discussed.
Abstract: Attempts to obtain a quantum theory of gravitation are reviewed. The essential ideas of those programmes on which extensive work has been done are discussed. Successes and difficulties of each of these programmes are described. The attempts are divided into two broad classes: those based on the techniques of canonical quantization and those based on the techniques of quantum field theory. The authors approach is rather geometrical, an approach which facilitates the comparison of various programmes.
102 citations
TL;DR: In this article, it was proved that the S-matrix satisfies the Bogolubov microcausality condition in each order in perturbation theory in a quantum field theory with nonlocal interaction, where the nonlocality is introduced with the help of form factors being entire analytical functions of the order 1/2.
Abstract: It is proved that theS-matrix satisfies the Bogolubov microcausality condition in each order in perturbation theory in a quantum field theory with nonlocal interaction, where the nonlocality is introduced with the help of form factors being entire analytical functions of the order 1/2.
74 citations
TL;DR: In this paper, the authors assume the existence of a conserved current which generates locally gauge transformations of first kind, and they are working in a local quantum Field Theory, where the fields are defined on a vector space where indefinite metric is allowed.
Abstract: We assume the existence of a conserved current which generates locally gauge transformations of first kind. We are working in a local quantum Field Theory, where the fields are defined on a vector space where indefinite metric is allowed.
TL;DR: In this article, the quantum-mechanical operator equation of motion for a point electron is derived, and it is shown that the electrostatic self-mass of the electron is zero in quantum mechanics.
Abstract: We derive the quantum-mechanical operator equation of motion for a point electron and show that (i) the electrostatic self-mass of a point electron is zero in quantum mechanics; (ii) the equation of motion does not admit runaway solutions; (iii) the correspondence limit of the solutions of the quantum-mechanical equation likewise does not display runaways; and (iv) the solutions do not violate the principle of causality in quantum mechanics.
TL;DR: In this paper, Hamilton's quaternions resurface once again to suggest relativistic generalizations of quantum theory and a new spin-12 wave equation, and they are used for vector analysis.
Abstract: Hamilton's ancient quaternion formalism gave rise to vector analysis. Quaternions resurface once again to suggest relativistic generalizations of quantum theory and a new spin-12 wave equation.
Book•
01 Jan 1974
TL;DR: The development of quantum theory in physics and chemistry has probably had more impact than any other development in twentieth-century science as discussed by the authors, and one of the few remaining scientists with first-hand knowledge of the events between 1900 and 1927 has comprehensively and accurately described the major discoveries, developments in thought and the people in this exciting period of scientific history.
Abstract: The development of quantum theory in physics and chemistry has probably had more impact than any other development in twentieth-century science. Professor Hund — one of the few remaining scientists with first-hand knowledge of the events between 1900 and 1927 has comprehensively and accurately described the major discoveries, developments in thought and the people in this exciting period of scientific history. Gordon Reece has made a lively and accurate translation of the German text.
TL;DR: In this article, the influence of the nuclear charge parameters, nuclear mass, degree of ionization on the value of the critical charge of the nucleus in almost critical fields is investigated.
Abstract: A careful investigation of different corrections to binding energies of electrons in almost critical fields is performed. We investigate quantitatively the influence of the nuclear charge parameters, nuclear mass, degree of ionization on the value of the critical charge of the nucleus. Rather qualitative arguments are given to establish the contribution of the quantumelectrodynamic corrections, which are found to be small. Some phenomenological modifications of QED are quantitatively investigated and found to be of negligible influence on the value of the critical field. For heavy ion collisions with Z1+Z2>Zcr the critical separations between ions are given as results of precise solutions of the relativistic two coulomb center problem. Corrections due to electron-electron interaction are considered. We find (with present theoretical accuracy) Zcr=173±2, in the heavy ion collisions Rcr(U-U) = 34.7±2 fm and Rcr (U-Cf)=47.7±2 fm. We shortly consider the possibility of spontaneous muon production in muonic supercritical fields.
TL;DR: The purpose in this article is to discuss some of the basic notions of quantum physics within the more general framework of operational statistics and empirical logic (as developed in Foulis and Randall, 1972, and Randall and Foul is, 1973).
Abstract: Our purpose in this article is to discuss some of the basic notions of quantum physics within the more general framework of operational statistics and empirical logic (as developed in Foulis and Randall, 1972, and Randall and Foulis, 1973). Empirical logic is a formal mathematical system in which the notion of an operation is primitive and undefined; all other concepts are rigorously defined in terms of such operations (which are presumed to correspond to actual physical procedures).
01 Jan 1974
TL;DR: In this article, the influence of given, classical electromagnetic fields on quantum electrodynamics was studied and a special case of QED in the presence of external (i.e. classical) fields was described.
Abstract: The theory to be described here is a special case of quantum electrodynamics (QED) in presence of external (i.e. classical) fields. We shall therefore begin with a short review of this more general topic. The problem of interest is here the influence of given, classical electromagnetic fields on QED. These fields are supposed to be strong, i.e. the coupling of charged particles to the fields is not to be considered as a small perturbation. Some motivation for studying such a theory can be derived from the following reasoning. It is known that a formal solution of QED can be formulated in terms of the free Green’s function in presence of an arbitrary external field. Any approximation to this function implies a corresponding one for QED. The study of special external field problems might give some insight in the machinery, which could help in the general case. To learn what happens if an expansion parameter is no longer small should be easier in special cases than in general (nobody knows really how to sum perturbation theory for a quantum field theory with interaction).
TL;DR: The purpose of the simultaneous measurement of noncommuting quantum observables can be viewed as the joint estimation of parameters of the density operator of the quantum system Joint estimation involves the application of a multiply parameterized operator-valued measure as discussed by the authors.
Abstract: The purpose of the simultaneous measurement of noncommuting quantum observables can be viewed as the joint estimation of parameters of the density operator of the quantum system Joint estimation involves the application of a multiply parameterized operator-valued measure An example related to the simultaneous estimation of the position and velocity of a particle is given Conceptual difficulties attending simultaneous measurement of noncommuting observables are avoided by this formation
TL;DR: In this article, it was shown that potentials in force-free regions have not only a nonlocal physically measurable significance (via, e.g., ∮A ·dl), but also have a necessary local significance via their quantum spread ΔA.
Abstract: In a sequel to our previous paper we discuss two thought experiments which show that potentials in force-free regions have not only a nonlocal physically measurable significance (via, e.g., ∮A ·dl), but, in singly connected portions of that region, also have a necessary local significance (via their quantum spread ΔA, which cannot be neglected). We then show, in continuation to the foregoing paper, how suchA arise “geometrically” as kinematic quantities associated with the transformation between “quantum-related” reference frames, e.g., when the relative frame velocities areq-numbers possessing a quantum spread.
TL;DR: In this paper, the Schrodinger equation only applies to sufficiently small systems which can be indiscernibly reproduced and possess assembly porperties, and different features of the classificatory results of quantum mechanics are discussed.
Abstract: Ten different, unexpected features of the classificatory results of quantum mechanics are discussed as well as the question whether the Schrodinger equation only applies to sufficiently small systems which can be indiscernibly reproduced and possess assembly porperties.
TL;DR: In this paper, a fully quantum treatment of the Rabi flipping was presented, and it was shown that for sufficiently large interaction times, the semi-classical approximation is inadequate even in the case of large field intensities.
TL;DR: In this paper, a perturbation method for quantum mechanical problems is presented in which the successive terms are obtained by algebraic recurrence relations without the use of any diagrams, and two examples, one an anharmonic oscillator with quartic self-interaction and one a spin with quadratic selfinteraction, are given to illustrate the use the recurrence relation perturbations method.
Abstract: A perturbation method for quantum mechanical problems is presented in which the successive terms are obtained by algebraic recurrence relations without the use of any diagrams Two examples, one an anharmonic oscillator with quartic self‐interaction, and one a spin with quadratic self‐interaction, are given to illustrate the use of this recurrence relation perturbation method
TL;DR: In this paper, the Gibbsian assemblage method was used to give a statistical description of one-particle experiments by means of a spinor field model, and it was shown that in the limiting case of pointlike nonrelativistic particles this method is equivalent to the quantum mechanical one, that is, the probability amplitude can be introduced satisfying all postulates of quantum mechanics.
Abstract: The simplest nonlinear spinor field equation admitting regular stationary solutions is considered. Following a causal interpretation of quantum mechanics, given by de Broglie in his double solution theory, these regular solutions must be regarded as describing the internal particle structure. Using this spinor field model, an attempt is made to give a statistical description of one-particle experiments by means of a Gibbsian assemblage method. It is shown that in the limiting case of pointlike nonrelativistic particles this method is equivalent to the quantum mechanical one, that is, the probability amplitude can be introduced satisfying all postulates of quantum mechanics.
Journal Article•
TL;DR: In this article, a uniqueness theorem for the momentum states of quantum mechanics is proved and a purely algebraic proof if given of the fact that in any irreducible representation of the CCR-algebra the von Neumann algebra generated by all translations is maximal abelian.
Abstract: In the algebraic formulation of quantum mechanics a class of states, called the momentum states are defined. They correspond to plane wave and wave packet states of ordinary quantum mechanics. A uniqueness theorem is proved for this class of states. Furthermore a purely algebraic proof if given of the fact that in any irreducible representation of the CCR-algebra the von Neumann algebra generated by all translations is maximal abelian.
TL;DR: In this paper, the genuine variational principle of macroscopic dissipative continua is generalized to complex scalar fields in the universal form of GAUSSian type, making it possible to extend the validity of the principle to the PS field of the non-relativistic SCHRODINGER equation, and to certain types of non-linear problems.
Abstract: The genuine variational principle of macroscopic dissipative continua is generalized to complex scalar fields in the universal form of GAUSSian type. The generalization makes it possible to extend the validity of the principle to the PS field of the non-relativistic SCHRODINGER equation, and to certain types of non-linear problems. Following MORSE's and FESHBACH's sequence of thoughtful ideas in reverse direction the fundamentals of an “abstract” transport theory, isomorphic with one-particle quantum theory, are developed and the possibility of interpreting the quantum theory by classical models is discussed. On the basis of new arguments, the impossibility of interpreting quantum mechanics in terms of classical transport theories (hydrodynamical model, diffusional and stochastic models) is established.