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Gentle perturbations (1971)

Radin, Charles

Springer

Communications in mathematical physics 23 (1971), S. 189-198

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ϱβ,A, of a canonical ensemble, ϱβ. The perturbations are chosen so as to preserve a relationship of the form ϱβ,A≦ constant ×ϱβ. Applications in ergodic theory and phase transitions are described.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01877741

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Particle lattice models and the dynamical instability of many-body systems (1975)

Radin, Charles

Springer

Communications in mathematical physics 44 (1975), S. 165-168

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract We consider the notion of dynamical instability of many-body systems wherein states, which are arbitrarily close initially, are not close at some other fixed time. In controlling the dynamics of interacting systems of identical Fermions moving on a lattice, we isolate a basic mechanism which causes instability.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01608828

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3

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The dynamical instability of nonrelativistic many-body systems (1977)

Radin, Charles

Springer

Communications in mathematical physics 54 (1977), S. 69-79

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract From computations in an exactly solvable many-body dynamical model we argue that, quite generally, a nonrelativistic quantum mechanics of infinitely many interacting particles must admit states without a global time evolution; equivalently, that the (quasi-local) observables of any such theory are not preserved in time by the Heisenberg dynamics. Our analysis is based on a dynamical instability common to interacting finite-particle systems.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01609837

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4

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Signal propagation in lattice models of quantum many-body systems (1978)

Radin, Charles

Springer

Communications in mathematical physics 62 (1978), S. 159-166

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract Upper and lower bounds are proven for the speed of propagation of general classes of physical signals in particle lattice models.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01248669

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5

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Crystals and quasicrystals: A continuum model (1986)

Radin, Charles

Springer

Communications in mathematical physics 105 (1986), S. 385-390

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract We construct the first model of particles in the plane with completely symmetric, short range, two body interactions which has quasiperiodic, but no periodic, ground states.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01205933

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Noncommutative mean ergodic theory (1971)

Radin, Charles

Springer

Communications in mathematical physics 21 (1971), S. 291-302

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract Sufficient conditions are given to obtain two levels of ergodic behavior for a wide class of dynamical systems. The notion of substate is emphasized and shown to lead to a natural generalization for noncommutative systems of the mean ergodic theorem onL 1. Applications to the time averaging of certain deviations from thermal equilibrium is mentioned.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01645751

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Dynamics of limit models (1973)

Radin, Charles

Springer

Communications in mathematical physics 33 (1973), S. 283-292

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract Using noncommutative integration theory, we show why certain singular behavior has been appearing in the dynamics of large quantum mechanical systems, and how to isolate the singularities.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01646741

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8

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Are there chaotic tilings? (1993)

Berend, Daniel ; Radin, Charles

Springer

Communications in mathematical physics 152 (1993), S. 215-219

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract We develop a class of examples in the form of tiling dynamical systems for use as toy models in statistical mechanics, to analyze the possible existence of disordered crystals. We give the first such models which are disordered in the sense of having no discrete spectrum.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02098297

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The isoperimetric problem for pinwheel tilings (1996)

Radin, Charles ; Sadun, Lorenzo

Springer

Communications in mathematical physics 177 (1996), S. 255-263

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ISSN: 1432-0916

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract In aperiodic “pinwheel” tilings of the plane there exist unions of tiles with ratio (area)/(perimeter)2 arbitrarily close to that of a circle. Such approximate circles can be constructed with arbitrary center and any sufficiently large radius. The existence of such circles follows from the metric on pinwheel space being almost Euclidean at large distances; ifP andQ are points separated by large Euclidean distanceR, then the shortest path along tile edges fromP toQ has lengthR+o(R).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02102438

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10

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Quaquaversal tilings and rotations (1998)

Conway, John H. ; Radin, Charles

Springer

Inventiones mathematicae 132 (1998), S. 179-188

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ISSN: 1432-1297

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. We construct a hierarchical tiling of 3 dimensional Euclidean space based on a triangular prism, using repeated rotations, about orthogonal axes, by angles 2π/m and 2π/n. To analyze the structure of the tiling we are led to determine the group G(m,n) generated by such a pair of rotations, for m=n=3 and for m=3, n=4.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002220050221

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