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  • 1
    Electronic Resource
    Electronic Resource
    On a non-Markoffian master equation (1969)
    Springer
    The European physical journal 223 (1969), S. 364-377 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Applying the non-Markoffian master equation discussed in a previous paper to the test case of an exactly solvable model we study here the theory of the damped harmonic oscillator. The results confirm the criterion for the applicability of the Born approximation in which our master equation is valid. On the other hand, the present paper generalizes Markoffian theories of the damped oscillator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01392866
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  • 2
    Electronic Resource
    Electronic Resource
    On a non-Markoffian master equation (1969)
    Springer
    The European physical journal 223 (1969), S. 353-363 
    Details
    ISSN: 1434-601X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider a microscopic system $$\mathfrak{S}$$ coupled to a bath $$\mathfrak{B}$$ and establish a non-Markoffian master equation for the reduced statistical operator of $$\mathfrak{S}$$ , valid in theBorn approximation. Discussing in detail theBorn approximation we find as a general condition for its validity that a certain “strength function” should not degenerate to one or more extremly sharp and high lines.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01392865
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  • 3
    Electronic Resource
    Electronic Resource
    Dichotomous noise forbids detailed balance (1991)
    Springer
    The European physical journal 84 (1991), S. 327-328 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Is is shown that for systems driven by dichotomous noise there is no detailed balance.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313555
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  • 4
    Electronic Resource
    Electronic Resource
    Quantum aspects of chaos for three-level atoms interacting with two harmonic oscillators (1990)
    Springer
    The European physical journal 79 (1990), S. 159-166 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We treat a simple generalization of the Jaynes-Cummings model to three-level atoms interacting with two harmonic oscillators. The model allows for classical chaos even in the rotating wave approximation, as was recently shown by Shepelyanski. Under conditions most favorable for classical chaos we find linear level repulsion à la Wigner.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01387837
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  • 5
    Electronic Resource
    Electronic Resource
    Taylor and Padé analysis of the level spacing distributions of random-matrix ensembles (1990)
    Springer
    The European physical journal 80 (1990), S. 153-158 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We construct the distributionP(S) of nearest-neighbor level spacings for the orthogonal, unitary, and symplectic ensembles of (Hermitian and unitary) random matrices in the limit of large dimension. The Taylor expansion ofP(S) aroundS=0 is given explicitly to arbitrarily high orders. By employing a diagonal Padé approximation we interpolate between the small-S behavior given by the Taylor expansion and the rigorously known asymptotic form at largeS.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390663
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  • 6
    Electronic Resource
    Electronic Resource
    Quantum effects of periodic orbits for the kicked top (1993)
    Springer
    The European physical journal 92 (1993), S. 221-233 
    Details
    ISSN: 1434-6036
    Keywords: 03.65.Sq ; 05.45.+b
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze traces of powers of the time evolution operator of a periodically kicked top. Semiclassically, such traces are related to periodic orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovered via a Fourier transform. A breakdown of the stationary phase approximation is detected. The quasi energy spectrum remains elusive due to lack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coefficients of the characteristic polynominal of the Floquet operator. Statistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01312181
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  • 7
    Electronic Resource
    Electronic Resource
    Statistics of self-crossings and avoided crossings of periodic orbits in the Hadamard-Gutzwiller model (2002)
    Springer
    The European physical journal 30 (2002), S. 189-206 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 05.45.Mt Semiclassical chaos (“quantum chaos”) – 03.65.Sq Semiclassical theories and applications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Employing symbolic dynamics for geodesic motion on the tesselated pseudosphere, the so-called Hadamard-Gutzwiller model, we construct extremely long periodic orbits without compromising accuracy. We establish criteria for such long orbits to behave ergodically and to yield reliable statistics for self-crossings and avoided crossings. Self-encounters of periodic orbits are reflected in certain patterns within symbol sequences, and these allow for analytic treatment of the crossing statistics. In particular, the distributions of crossing angles and avoided-crossing widths thus come out as related by analytic continuation. Moreover, the action difference for Sieber-Richter pairs of orbits (one orbit has a self-crossing which the other narrowly avoids and otherwise the orbits look very nearly the same) results to all orders in the crossing angle. These findings may be helpful for extending the work of Sieber and Richter towards a fuller understanding of the classical basis of quantum spectral fluctuations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1140/epjb/e2002-00374-7
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  • 8
    Electronic Resource
    Electronic Resource
    Renormalization group transformation for the master equation of a kinetic Ising chain (1979)
    Springer
    The European physical journal 35 (1979), S. 281-285 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We define and solve a dynamical real-space renormalization group transformation for the master equation of a kinetic Ising model in one dimension. The exactly solvable model we treat has the dynamical exponentz=2. We show that spin flip rates differing from Glauber's choice may have exponentsz differing from 2. A particular model which hasz=4 is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01319850
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  • 9
    Electronic Resource
    Electronic Resource
    Universality classes for one dimensional kinetic Ising models (1980)
    Springer
    The European physical journal 40 (1980), S. 219-226 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We use variational techniques to construct upper and lower bounds for the dynamical exponentz of kinetic Ising models. The most important universality class is shown to havez=2. We find larger values ofz, however, for continuous sets of both pure single-spin-flip and double-spin-flip models. For pure double-spin flips with order parameter conservation we findz≧5; this bound is consistent with a corresponding transport coefficient which vanishes at the zero-temperature critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01294531
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  • 10
    Electronic Resource
    Electronic Resource
    Statistics of complex levels of random matrices for decaying systems (1992)
    Springer
    The European physical journal 88 (1992), S. 359-370 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present analytical and numerical results for the level density of a certain class of random non-Hermitian matrices ℋ=H+iГ. The conservative partH belongs to the Gaussian orthogonal ensemble while the damping piece Г is quadratic in Gaussian random numbers and may describe the decay of resonances through various channels. In the limit of a large matrix dimension the level density assumes a surprisingly simple dependence on the relative strength of the damping and the number of channels. Moreover, we identify situations with cubic repulsion between the complex eigenvalues of ℋ, to within a logarithmic correction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01470925
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