Geometric structure and information change in phase transitions

It is shown that in the case of spontaneous breaking of the original gauge symmetry, a dynamic rearrangement of vacuum may lead to the formation of some anisotropic condensates. The appearance of such condensates causes the respective phase transitions in the geometric structure of space-time and creates a flat anisotropic, i.e. Finslerian event space. Actually there arises either a flat relativistically invariant Finslerian space with partially broken 3D isotropy, i.e. axially symmetric space, or a flat relativistically invariant Finslerian space with entirely broken 3D isotropy. The fact that any entirely anisotropic relativistically invariant Finslerian event space belongs to a 3-parameter family of such spaces gives rise to a fine structure of the respective geometric phase transitions. In the present paper the fine structure of the geometric phase transitions is studied by classifying all the metric states of the entirely anisotropic event space and the respective mass shell equations.

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On the possibility of phase transitions in the geometric structure of space-time

Physics Letters A ◽

10.1016/s0375-9601(98)00293-x ◽

1998 ◽

Vol 244 (4) ◽

pp. 222-228 ◽

Cited By ~ 33

Author(s):

G.Yu. Bogoslovsky ◽

H.F. Goenner

Keyword(s):

Phase Transitions ◽

Geometric Structure ◽

Space Time

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Information Geometry of Nonlinear Stochastic Systems

Entropy ◽

10.3390/e20080550 ◽

2018 ◽

Vol 20 (8) ◽

pp. 550 ◽

Cited By ~ 7

Author(s):

Rainer Hollerbach ◽

Donovan Dimanche ◽

Eun-jin Kim

Keyword(s):

Geometric Structure ◽

Stochastic Systems ◽

Power Laws ◽

Information Geometry ◽

Scaling Exponent ◽

Stochastic Noise ◽

Initial Stage ◽

Constant Rate ◽

Information Change ◽

Transient Relaxation

We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and different strength D of δ-correlated stochastic noise. We identify the three main stages consisting of nondiffusive evolution, quasi-linear Gaussian evolution and settling into stationary PDFs. The strength of stochastic noise is shown to play a crucial role in determining these timescales as well as the peak amplitude and width of PDFs. From time-evolution of PDFs, we compute the rate of information change for a given initial PDF and uniquely determine the information length L(t) as a function of time that represents the number of different statistical states that a system evolves through in time. We identify a robust geodesic (where the information changes at a constant rate) in the initial stage, and map out geometric structure of an attractor as L(t→∞)∝μm, where μ is the position of an initial Gaussian PDF. The scaling exponent m increases with n, and also varies with D (although to a lesser extent). Our results highlight ubiquitous power-laws and multi-scalings of information geometry due to nonlinear interaction.

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Electron Microscopy of Graphite Intercalation Compounds

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100055564 ◽

1982 ◽

Vol 40 ◽

pp. 544-545

Author(s):

G. Timp ◽

L. Salamanca-Riba ◽

L.W. Hobbs ◽

G. Dresselhaus ◽

M.S. Dresselhaus

Keyword(s):

Electron Microscopy ◽

Phase Transitions ◽

Domain Wall ◽

Intercalation Compounds ◽

Lattice Plane ◽

Wall Model ◽

Graphite Intercalation Compounds ◽

Fundamental Symmetry ◽

Graphite Intercalation

Electron microscopy can be used to study structures and phase transitions occurring in graphite intercalations compounds. The fundamental symmetry in graphite intercalation compounds is the staging periodicity whereby each intercalate layer is separated by n graphite layers, n denoting the stage index. The currently accepted model for intercalation proposed by Herold and Daumas assumes that the sample contains equal amounts of intercalant between any two graphite layers and staged regions are confined to domains. Specifically, in a stage 2 compound, the Herold-Daumas domain wall model predicts a pleated lattice plane structure.

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Multiple phase transitions investigated by high-speed TEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100175880 ◽

1990 ◽

Vol 48 (4) ◽

pp. 550-551

Author(s):

Oleg Bostanjoglo ◽

Peter Thomsen-Schmidt

Keyword(s):

Phase Transitions ◽

High Speed ◽

Short Exposure ◽

Semiconductor Film ◽

Time Resolved ◽

Short Exposure Time ◽

Multiple Phase ◽

Model Substance ◽

History Of ◽

Electron Image

Thin GexTe1-x (x = 0.15-0.8) were studied as a model substance of a composite semiconductor film, in addition being of interest for optical storage material. Two complementary modes of time-resolved TEM were used to trace the phase transitions, induced by an attached Q-switched (50 ns FWHM) and frequency doubled (532 nm) Nd:YAG laser. The laser radiation was focused onto the specimen within the TEM to a 20 μm spot (FWHM). Discrete intermediate states were visualized by short-exposure time doubleframe imaging /1,2/. The full history of a transformation was gained by tracking the electron image intensity with photomultiplier and storage oscilloscopes (space/time resolution 100 nm/3 ns) /3/. In order to avoid radiation damage by the probing electron beam to detector and specimen, the beam is pulsed in this continuous mode of time-resolved TEM,too.Short events ( <2 μs) are followed by illuminating with an extended single electron pulse (fig. 1c)

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