Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Nonlinear quantum mechanics for systems of composite spin

Ronald Lee Walsworth, Isaac F. Silvera

Published Jul 1, 1990• 2 citations
Publisher

Abstract

A nonlinear generalization of quantum mechanics for internal (spin) degrees of freedom has recently been developed by Weinberg [Phys. Rev. Lett. 62, 485 (1989); Ann. Phys. (N.Y.) 194, 336 (1989)]. We extend this theory to systems of composite, or multivalued, spin, such as atoms and molecules. Results for the generalized Hamiltonian function, energy eigenvalues, and state-vector time dependence are found to be similar for single- and multivalued spin systems, with the important difference that states of spin 0 or 1/2 can exhibit observable nonlinear behavior in a composite spin system. Examples of the application of the composite spin analysis are given for the ground-state hyperfine structure of the hydrogen and deuterium atoms.

DOI
10.1103/physreva.42.63

Related papers

Atomic Physics Tests of Nonlinear Quantum Mechanics

J. J. Bollinger, Daniel J. Heinzen, Wayne M. Itano +2 more

Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. set limits less than 10 pHz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than- on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. nonlinear addition to quantum mechanics violates causality is discussed. The experiments The possibility that a

•Jan 1, 1990•0 citations

Test of the linearity of quantum mechanics in an atomic system with a hydrogen maser

Ronald Lee Walsworth, Isaac F. Silvera, Edward M. Mattison +1 more

We extend a nonlinear generalization of quantum mechanics, recently formulated by Weinberg, to systems of composite spin, such as atoms. We have used hydrogen (H) masers to set a limit of 3.7\ifmmode\times\else\texttimes\fi{}${10}^{20}$ eV (8.9 \ensuremath{\mu} Hz) on the magnitude of a nonlinear correction to the quantum mechanics of atomic spins. This result is of comparable magnitude to the limit recently set in a single-valued (nuclear) spin system. In the absence of nonlinear effects, the experiment provides a new and stringent test of H-maser clock performance and the applicability of standard maser theory.

Physical Review Letters•May 28, 1990•61 citations

Composite‐system models

Douglas J. Klein, Josep M. Oliva

Abstract Composite many‐electron systems are considered in terms of the wave‐functions for the different component subsystems (e.g., atoms). In this weak‐interaction limit, there may be degrees of freedom, which arise from that of the degeneracies of the wave‐functions for each of the isolated subsystems, and which then are describable in terms of an effective Hamiltonian for the couplings and liftings of these degeneracies in the composite system. The representation of an ordinary Schrödinger Hamiltonian in such a 0‐order model space is developed in the context of an example of a (possibly macroscopically large) set of H atoms interacting with one another, to obtain a Heisenberg spin‐Hamiltonian, which is formally “complete” in not neglecting any higher‐order permutations. At the same time, the interactions are hierarchically ordered to manifest the more important ones first, all in a “linked” size‐consistent manner, avoiding various earlier‐encountered “catastrophes.” A classical electrostatic interpretation of the higher order exchange matrix elements is made, and some novel spin‐coupling dependences are found with a decay like an inverse power‐law range (rather than exponential). © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

International Journal of Quantum Chemistry•Sep 23, 2010•3 citations

Quantum mechanics of composite objects with internal entanglement

Fumika Suzuki

Although many quantum mechanics problems of a point particle have been well understood, the realistic physical model is often a composite object consisting of particles bound together, and its quantum mechanics is an important problem with applications in many areas of physics. Unlike a point particle, a composite object possesses internal structure described by some degrees of freedom which are often entangled with each other. We call the entanglement among these degrees of freedom ``internal entanglement'', to distinguish it from any other entanglement they may share with an external object. Examples of internal entanglement include the entanglement between a vibrational and a rotational mode of a molecule, and that between its position and its internal clock-state etc. In this thesis, we study quantum mechanics of composite objects by focusing on the effects of internal entanglement. We first look at the tunnelling of a diatomic molecule type composite object through a half-silvered mirror in continuum space and observe that its spatial superposition state made by the mirror can decohere by emission of radiation due to the fact that its internal degrees of freedom are entangled with radiation fields, and that there exists entanglement between its position and its internal (i.e., relative position) degrees of freedom. Secondly, we study its lattice analog in molecular crystals, namely we replace the diatomic molecule by a biexicton, and the mirror by an impurity. We find that discreteness of a lattice makes the wave vector of a biexicton and the relative distance between two excitons of it entangled with each other. We investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics. Finally we propose a possible application of our study of internal entanglement to the Anderson model of a composite quasiparticle.

•Jan 1, 2017•1 citation

Nonlinear Schrödinger equation and two-level atoms

Marek Czachor

Starting with the same form of atomic nonlinearity, Weinberg [Ann. Phys. (NY) 194, 336 (1989)] and W\'odkiewicz and Scully [Phys. Rev. A 42, 5111 (1990)] obtained contradictory results concerning an evolution of the atomic inversion w in a two-level atom in Weinberg's nonlinear quantum mechanics: If the atom is initially in a ground state then either the evolution of w (1) can be linear if one uses a nonlinear generalization of the Jaynes-Cummings Hamiltonian, or (2) is always nonlinear if one uses the nonlinear Bloch equations derived from the nonlinear atomic Hamiltonian function. It is shown that the difference is rooted in inequivalent descriptions of the composite ``atom-plus-field'' system. The linear evolution of w results from a ``faster-than-light communication'' between the atom and the field. If one applies a description without the ``faster-than-light telegraph'' then the calculations based on a suitably modified Jaynes-Cummings Hamiltonian lead to the same dynamics of w as is found in semiclassical calculations based on Bloch equations. It is shown also that a nonlinear quantum mechanics based on a nonlinear Schr\"odinger equation does not possess a natural probability interpretation.

arXiv:quant-ph/9501007•Physical Review A•Mar 1, 1996•28 citations

Quantum-classical hybrid dynamics – a summary

Hans-Thomas Elze

A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of classical Hamiltonian mechanics suitably extended to quantum mechanics.

arXiv:1306.4480•Journal of Physics Conference Series•Jun 10, 2013•17 citations
A nonlinear generalization of quantum mechanics for internal (spin) degrees of freedom has recently been developed by Weinberg [Phys. Rev. Lett. 62, 485 (1989); Ann. Phys. (N.Y.) 194, 336 (1989)]. We extend this theory to systems of composite, or multivalued, spin, such as atoms and molecules. Results for the generalized Hamiltonian function, energy eigenvalues, and state-vector time dependence are found to be similar for single- and multivalued spin systems, with the important difference that states of spin 0 or 1/2 can exhibit observable nonlinear behavior in a composite spin system. Examples of the application of the composite spin analysis are given for the ground-state hyperfine structure of the hydrogen and deuterium atoms.
Atomic physics experiments which test a nonlinear generalization of quantum mechanics recently formulated by Weinberg are described. The experiments search for a dependence of hyperfine transition frequencies or nuclear spin precession frequencies on the relative populations of the hyperfine or nuclear spin states. set limits less than 10 pHz on the size of the possible nonlinear contributions to these frequencies. In some cases this can be interpreted as a limit of less than- on the fraction of binding energy per nucleon that could be due to a nonlinear correction to a nuclear Hamiltonian. nonlinear addition to quantum mechanics violates causality is discussed. The experiments The possibility that a
We extend a nonlinear generalization of quantum mechanics, recently formulated by Weinberg, to systems of composite spin, such as atoms. We have used hydrogen (H) masers to set a limit of 3.7\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 eV (8.9 \ensuremath{\mu} Hz) on the magnitude of a nonlinear correction to the quantum mechanics of atomic spins. This result is of comparable magnitude to the limit recently set in a single-valued (nuclear) spin system. In the absence of nonlinear effects, the experiment provides a new and stringent test of H-maser clock performance and the applicability of standard maser theory.
Abstract Composite many‐electron systems are considered in terms of the wave‐functions for the different component subsystems (e.g., atoms). In this weak‐interaction limit, there may be degrees of freedom, which arise from that of the degeneracies of the wave‐functions for each of the isolated subsystems, and which then are describable in terms of an effective Hamiltonian for the couplings and liftings of these degeneracies in the composite system. The representation of an ordinary Schrödinger Hamiltonian in such a 0‐order model space is developed in the context of an example of a (possibly macroscopically large) set of H atoms interacting with one another, to obtain a Heisenberg spin‐Hamiltonian, which is formally “complete” in not neglecting any higher‐order permutations. At the same time, the interactions are hierarchically ordered to manifest the more important ones first, all in a “linked” size‐consistent manner, avoiding various earlier‐encountered “catastrophes.” A classical electrostatic interpretation of the higher order exchange matrix elements is made, and some novel spin‐coupling dependences are found with a decay like an inverse power‐law range (rather than exponential). © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010
Although many quantum mechanics problems of a point particle have been well understood, the realistic physical model is often a composite object consisting of particles bound together, and its quantum mechanics is an important problem with applications in many areas of physics. Unlike a point particle, a composite object possesses internal structure described by some degrees of freedom which are often entangled with each other. We call the entanglement among these degrees of freedom ``internal entanglement'', to distinguish it from any other entanglement they may share with an external object. Examples of internal entanglement include the entanglement between a vibrational and a rotational mode of a molecule, and that between its position and its internal clock-state etc. In this thesis, we study quantum mechanics of composite objects by focusing on the effects of internal entanglement. We first look at the tunnelling of a diatomic molecule type composite object through a half-silvered mirror in continuum space and observe that its spatial superposition state made by the mirror can decohere by emission of radiation due to the fact that its internal degrees of freedom are entangled with radiation fields, and that there exists entanglement between its position and its internal (i.e., relative position) degrees of freedom. Secondly, we study its lattice analog in molecular crystals, namely we replace the diatomic molecule by a biexicton, and the mirror by an impurity. We find that discreteness of a lattice makes the wave vector of a biexicton and the relative distance between two excitons of it entangled with each other. We investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics. Finally we propose a possible application of our study of internal entanglement to the Anderson model of a composite quasiparticle.
Starting with the same form of atomic nonlinearity, Weinberg [Ann. Phys. (NY) 194, 336 (1989)] and W\'odkiewicz and Scully [Phys. Rev. A 42, 5111 (1990)] obtained contradictory results concerning an evolution of the atomic inversion w in a two-level atom in Weinberg's nonlinear quantum mechanics: If the atom is initially in a ground state then either the evolution of w (1) can be linear if one uses a nonlinear generalization of the Jaynes-Cummings Hamiltonian, or (2) is always nonlinear if one uses the nonlinear Bloch equations derived from the nonlinear atomic Hamiltonian function. It is shown that the difference is rooted in inequivalent descriptions of the composite ``atom-plus-field'' system. The linear evolution of w results from a ``faster-than-light communication'' between the atom and the field. If one applies a description without the ``faster-than-light telegraph'' then the calculations based on a suitably modified Jaynes-Cummings Hamiltonian lead to the same dynamics of w as is found in semiclassical calculations based on Bloch equations. It is shown also that a nonlinear quantum mechanics based on a nonlinear Schr\"odinger equation does not possess a natural probability interpretation.