*Robert Alicki and Mark Fannes*

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in ...
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A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in deterministic quantum systems based on a spin chain model. The starting point is an operational partition that is refined in the course of time. To each partition corresponds a correlation matrix and the dynamics lead eventually to a shift-invariant state on a quantum spin chain with its associated entropy. General properties and bounds are proved, which allow for the computation of the entropy in a number of simple model systems such as finite systems, shift dynamics on a quantum spin chain, free shifts, and Powers–Price shifts.Less

A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in deterministic quantum systems based on a spin chain model. The starting point is an operational partition that is refined in the course of time. To each partition corresponds a correlation matrix and the dynamics lead eventually to a shift-invariant state on a quantum spin chain with its associated entropy. General properties and bounds are proved, which allow for the computation of the entropy in a number of simple model systems such as finite systems, shift dynamics on a quantum spin chain, free shifts, and Powers–Price shifts.

*Helmut Rauch and Samuel A. Werner*

- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198712510
- eISBN:
- 9780191780813
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198712510.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and ...
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Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and the Schrödinger wave equation which involves a scalar wave function. Nevertheless, a description of interference effects requires the solution of a Helmholtz scalar wave equation in both cases. Gravitational, inertial, and motional effects lead to rather large phase shifts in neutron interferometry. This chapter describes how the quantum phase shift is calculated, usually by evaluating the action as an integral over the Lagrangian. A connection to relativity theory is given when the Compton frequency depending on the mass of the neutron is taken as a physical quantity. It concludes with a list of the approximately 40 neutron interferometry experiments carried out in various laboratories worldwide, which form the subject of this book.Less

Electromagnetic optical phenomena are generally understood via Maxwell’s equations for the electric and magnetic vector fields. Neutron optical phenomena are based upon de Broglie matter waves and the Schrödinger wave equation which involves a scalar wave function. Nevertheless, a description of interference effects requires the solution of a Helmholtz scalar wave equation in both cases. Gravitational, inertial, and motional effects lead to rather large phase shifts in neutron interferometry. This chapter describes how the quantum phase shift is calculated, usually by evaluating the action as an integral over the Lagrangian. A connection to relativity theory is given when the Compton frequency depending on the mass of the neutron is taken as a physical quantity. It concludes with a list of the approximately 40 neutron interferometry experiments carried out in various laboratories worldwide, which form the subject of this book.

*Helmut Rauch and Samuel A. Werner*

- Published in print:
- 2015
- Published Online:
- March 2015
- ISBN:
- 9780198712510
- eISBN:
- 9780191780813
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198712510.003.0008
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The first experiment in which gravity and quantum mechanics play simultaneous important roles was carried out by Colella, Overhauser, and Werner (COW). This and subsequent versions of this experiment ...
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The first experiment in which gravity and quantum mechanics play simultaneous important roles was carried out by Colella, Overhauser, and Werner (COW). This and subsequent versions of this experiment are described in this chapter. Because this experiment was carried out on the surface of our rotating Earth, an additional phase shift was subsequently observed. It is the matter wave analogue to the optical Sagnac effect. Neutrons under Bragg reflecting conditions have their internal wave vectors lying on a Brillioun zone boundary, and will experience an altered force described by an effective mass in a manner directly analogous to electrons in a crystal. The phase shift of neutrons upon passing through moving matter analogous to the optical Fizeau effect requires an energy-dependent scattering length as has been observed with a rotating wheel of Sm metal. There is an additional phase shift of neutrons when the boundaries of a material medium move with respect to a neutron beam. Connections to general relativity theory are discussed.Less

The first experiment in which gravity and quantum mechanics play simultaneous important roles was carried out by Colella, Overhauser, and Werner (COW). This and subsequent versions of this experiment are described in this chapter. Because this experiment was carried out on the surface of our rotating Earth, an additional phase shift was subsequently observed. It is the matter wave analogue to the optical Sagnac effect. Neutrons under Bragg reflecting conditions have their internal wave vectors lying on a Brillioun zone boundary, and will experience an altered force described by an effective mass in a manner directly analogous to electrons in a crystal. The phase shift of neutrons upon passing through moving matter analogous to the optical Fizeau effect requires an energy-dependent scattering length as has been observed with a rotating wheel of Sm metal. There is an additional phase shift of neutrons when the boundaries of a material medium move with respect to a neutron beam. Connections to general relativity theory are discussed.