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1$B7n(B25$BF|(B15$B;~H>$+$i(B | $BM}3XIt(B1$B9f4[(B447 | Tomio Petrosky (The University of Texas) | Alien Baltan tye of fractal spectrum of an irreversible collision operator for a.AN molecular chains |

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[1] A. Nishino, T. Imamura and N. Hatano, Phys. Rev. Lett. 102 (2009) 146803.

[2] V. M. Filyov and P. B. Wiegmann, Phys. Lett. A 76 (1980) 283.

[3] P. Mehta and N. Andrei, Phys. Rev. Lett. 96 (2006) 216802.

[4] B. Doyon, Phys. Rev. Lett. 99 (2007) 076806.

[5] A. Golub, Phys. Rev. B 76 (2007) 193307.

[6] E. Boulat and H. Saleur and P. Schmitteckert, Phys. Rev. Lett. 101 (2008) 140601.

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**

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**$B>l=j!'(B**$BM}3XIt(B1$B9f4[(B338

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**

We address universality of quantum-classical correspondence of chaos when symmetries change. We first consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of the spectral correlation is calculated by using the semiclassical periodic-orbit theory.

Then we show random matrix results are reproduced. This physically proves long-standing problem called Bohigas, Giannoni, and Schmit(BGS) conjecture, in this regime.

Next we try to consider GOE-GSE crossover. In this domain, Random matrix results are not known. We show that semiclassical approach can give new results in this regime.

As an application, chaotic transport is considered in GOE-GSE crossover regime. This regime is relevant in semiconductor with Rashba coupling where weak spin-orbit coupling is induced by applying electric fields. Then conductance, conductance fluctuation, and shot noise etc, are systematically calculated.

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frustrated XY model$B$O<'>lCf$N(BJosephson$B7k9gG[Ns$N%b%G%k$H$7$FCN$i$l$F$*$j!"<'B+3J;R$NM;2rE>0\$r5-=R$G$-$k!#(B $BK\%;%_%J!<$G$O$3$N%b%G%k$N!"=D$H2#$N%\%s%I$G7k9gDj?t$,0[$J$k>l9g$K$D$$$F!"$=$N0U5A$H?tCM%7%_%e%l!<%7%g%s$N7k2L$r>R2p$9$k!#(B

$B0[J}@-$N8z2L$O(Bfilling(1$B%W%i%1%C%H$"$?$j$NJ?6Q(Bvortex$B?t(B)$B$,L5M}?t$N$H$-$K82Cx$G!"(B $BEyJ}E*$J>l9g%<%m$G$"$C$?M;2r$NE>0\29EY$,L58B>.$N0[J}@-$K$h$C$FM-8B$K$J$k!#(B

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$B%7%c%Z%m%K%s$O!$JQ@-$7$?%?%s%Q%/uBV$N%(%s%H%m%T!<$r8:>/$5$;!$@^$l>v$_$rB%?J$9$k8z2L$,$"$k$3(B $B$H!$$^$?!$3F%?%s%Q%/v$_$rB%?J$9$k(B)$BH"%5%$%:(B" $B$,$"$k$3$H$r<($7$?!%(B

ref.: Takagi, Koga, and Takada (2003) Proc. Natl. Acad. Sci. USA, vol.100, pp.11367

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**$B9V1i Cristian Enachescu(Alexandru Ioan Cuza University)
**

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**$B9V1i Per Arne Rikvold(Florida State University)
**

I will discuss an individual-based, evolutionary model of ecological community assembly in a spatially extended landscape. Concretely, the landscape consists of a square lattice of local communities that together form a metacommunity. The reproduction rate of the individuals of a species depends on their interactions with the other species present in the local community. Individuals with reproduction rates below a threshold disperse with high probability to a randomly chosen neighboring community. At a critical value of the threshold, a discontinuous nonequilibrium phase transition takes place. Below the transition the metacommunity consists of effectively isolated, dissimilar local communities, each consisting of a small number of species that interact through mutually beneficial (mutualistic) interactions. Above the transition the local communities become similar, giving rise to a largely homogeneous metacommunity in which the interspecies interactions also include mutually deleterious (competitive) and predator/prey interactions.

We discuss both the simple case in which the population size in each local community is regulated by a spatially homogeneous carrying capacity, and a more complicated case in which the carrying capacity varies along a smooth spatial gradient.

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**

In low-dimensional quantum antiferromagnets, such as Spin-Peierls materials and Haldane systems, non-magnetic spin gap state is realized by strong quantum fluctuations. It is known that when non-magnetic impurities are doped into such state, so-called "impurity-induced antiferromagnetic long-range order" emerges at low-temperatures due to the competition between quantum nature, randomness, and lattice fluctuations. In this seminar, we introduce a new efficient quantum Monte Carlo method for spin-Peierls system and discuss the effects of quantum fluctuations and dimensionality on the spin-Peierls transition as well as on the impurity-induced long-range order.

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**

The main purpose of the present paper is to analyze the conductance of an $N$-site quantum dot with multiple semi-infinite leads. First, we obtain a simple conductance formula that contains only the local density of discrete eigenstates and the local density of states of the leads, where the discrete eigenstates consist of the bound states, the anti-bound states, the resonant states and the anti-resonant states. In other words, the conductance is given by the sum of all the simple poles in the complex energy plane. To our knowledge, this is the first time the effect of resonances on the conductance is shown exactly. Second, by using the above conductance formula, we show that the asymmetry of the Fano conductance peak arises from three origins, namely, from the interference between a resonant state and an anti-resonant state, between a resonant state and a bound state, and between two different states. Finally, we microscopically derive three types of the Fano parameter from the local density of discrete eigenstates, whereas in previous studies in the literature, the Fano parameter mainly has been used phenomenologically to describe the shape of an asymmetric conductance peak.

This is a collaboration with Keita Sasada and Gonzalo Ordonez.

http://jp.arxiv.org/abs/0905.3953

**$BF|;~!'(B**7$B7n(B14$BF|(B(Tue)15$B;~$h$j(B

**$B>l=j!'(B**$BM}3XIt(B4$B9f4[(B1320

**$B9V1i Ferenc Kun(University of Debrecen, Hungary)
**

The fracture of heterogeneous materials under various types of external loads is an important scientific problem with a broad spectrum of technological applications. Due to the relevance of disorder, the application of statistical physics and computer simulation of mesocopic models provided novel insight into fracture phenomena complementing the traditional engineering approaches.

We present the motivation of the application of statistical physics in this field, and give an overview of the most important modelling approaches such as the fiber bundle model and the discrete element model. We review recent findings on the creep rupture, fatigue and dynamic fracture of heterogeneous materials.

**$BF|;~!'(B**7$B7n(B21$BF|(B(Tue)15$B;~$h$j(B

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**$B9V1i Timothy Ziman (Institut Laue Langevin and CNRS, Grenoble)
**

There is an active search for useful substances with room temperature ferromagnetism and semiconducting properties, obtained by diluting semiconducting materials with impurities. Understanding of doped III-V materials in particular has improved greatly and it is now possible to compare different theoretical models with more controlled experiments. Another aspect is to find simple models which capture the essential ingredients for ferromagnetism which may help looking for new materials. I will discuss these isues with particular reference to questions that may be clarified by scattering experiments: microscopic couplings, doping dependence of samples, inhomogeneities and the like. I will also discuss ideas related to the less established possibility of \u201cdefect-induced ferromagnetism\u201d in oxides in which obviously magnetic dopants are not present.

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**$B9V1i Frederic Mila (University of Lausanne)
**

In quantum magnets, the magnetization process can be described as filling up the system with magnetic particles that behave as as hard-core bosons, and the magnetic field plays the role of the chemical potential. The high tunability of this effective chemical potential as compared to other systems opens the way to new investigations of lattice bosonic models, especially when dealing with frustrated magnets. In this talk, I will review a number of recent successes in this field, with emphasis on two compounds where remarkable phases have been identified, the plateau system SrCu2(BO3)2 and the bilayer system BaCuSi2O6 (Han purple), and I will discuss the relevant theoretical concepts to understand the physics of these compounds, namely magnetization plateaux, supersolid phases, and dimensional reduction.

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**$B9V1i Stefan Luding(Multi Scale Mechanics, UTwente, Netherlands)
**

In the limiting case of dilute and almost elastic granular gases the framework of kinetic theory can be applied successfully. We start from and apply various physical and numerical corrections. Traditional kinetic theory alone is not sufficient since, in realistic low density is usually co-existing with very high density. Furthermore, additional non-linear phenomena and material properties are important, involving:

(i) multi-particle interactions and elasticity

(ii) strong dissipation,

(iii) friction,

(iv) long-range forces and wet contacts

(v) wide particle size-distributions, and

(vi) various particle shapes.

After a review of recent progress on realistic models for granular starting from an elastic, frictionless and monodisperse hard sphere the (continuum) balance equations of mass, momentum and energy (at Navier-Stokes level) are the starting point for further studies concerning especially the 'global' equation of state at all densities, the presence of multi-particle collisions, and energy input into dissipative granular systems.

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**$B9V1i $BEgED(B $B>0(B (The University of Tokyo, Japan)
**

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ref.) T. Shimada et al., Phys. Rev. E 80, 020301(R) (2009)

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**$B9V1i $BBgJ?(B $BE0(B(Sony Computer Science Laboratories)
**

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$B!V%N%$%:$HCY$l$N?tM}!W!JBgJ?E0Cx!"6&N)=PHG!"#2#0#0#6G/#17n!K(B.

"Balancing with Vibration", J. Milton, et. al. , Plos One(http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0007427)

$B!V;~4V<4>e$NHs6I=j@-$H$f$i$.!WBgJ?E0!"F|K\J*M}3X2q;o(B vol. 60, 260 (2007/4).

"Stochasticity and Non-locality of Time", T. Ohira, Physica A, Vol 379, 483 (2007).

"Resonance with Noise and Delay", T. Ohira and Y. Sato, Physical Review Letters, vol. 82, 2811 (1999).

"Delayed Stochastic Systems", T. Ohira and T. Yamane, Physical Review E, vol. 61, 1247 (2000).

**$BF|;~!'(B**11$B7n(B16$BF|(B($B7n(B)16:00$B$h$j(B

**$B>l=j!'(B**$BM}3XIt(B1$B9f4[(B447$B9f<<(B

**$B9V1i Eric Vincent(CEA Saclay)
**

In this talk, we shall introduce spin glasses and review the general experimental features of their glassy dynamics [1]. We shall use spin glasses as a guideline for enlightening the behaviour of a few other disordered systems, like suspensions of interacting magnetic nanoparticles (which are presently under investigation [2]), structural or polymer glasses, gels, etc.

Spin glasses are model magnetic systems in which the interactions are disordered and frustrated, due to a random dilution of magnetic ions. Below their glass temperature

Similar aging, rejuvenation and memory phenomena can be observed in many other glassy systems [1,2], making the spin glasses conceptually simple examples for the study of out-of-equilibrium dynamics in disordered systems.

references

[1] see references in E. Vincent, Lecture notes in Physics

[2] D. Parker, V. Dupuis, F. Ladieu, J.-P. Bouchaud, E. Dubois, R. Perzynski, and E. Vincent, Phys. Rev. B

E. Wandersman, V. Dupuis, E. Dubois, R. Perzynski, S. Nakamae and E. Vincent, Europhys. Lett

S. Nakamae, Y. Tahri, C. Thibierge, D. L$B!G(BHôte, E. Vincent, V. Dupuis, E. Dubois, and R. Perzynski, J. Appl. Phys.

[3] J.-P. Bouchaud, V. Dupuis, J. Hammann and E. Vincent, Phys. Rev. B

F. Bert, V. Dupuis, E. Vincent, J. Hammann and J.-P. Bouchaud, Phys. Rev. Lett.

[4] S. Miyashita and E. Vincent, Eur. Phys. J. B

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**

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references

[1] T. S. Komatsu and N. Nakagawa, Phys. Rev. Lett. v.100, 030601 (2008), "Expression for the stationary distribution in nonequilibrium steady states".

[2] T. S. Komatsu, N. Nakagawa, S. Sasa and H. Tasaki, J. Stat. Phys. v.134, 401 (2009), "Representation of Nonequilibrium Steady States in Large Mechanical Systems".

[3] T. S. Komatsu, N. Nakagawa, S. Sasa and H. Tasaki, Phys. Rev. Lett. v.100, 230602 (2008), "Steady-state thermodynamics for heat conduction: microscopic derivation".

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A characteristic feature of complex systems is an evolution dynamics with diversity and variety. It is cleary observed in biological, ecological, social and economic systems. Starting from simple models of molecules and/or agents, such evolution behaviors are studied with computer simulations. From microscopic side, it is shown that open reacting systems can go beyond thermal fluctuation and find rare and thin ways. This is helped by broad log-normal distributions and accumulation of unused resources.

Such behavior is an example how systems find and acquire diversity beyond equilibrium state. From macroscopic side, tolerance for other species are necessary so that a system show evolving dynamics. Simple models of ecoevolution reveal a universal feature: a skewed life-time distribution, which is well fitted both by a *q*-exponential function or by a stretched exponential function.

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[1] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 146802 (2005); ibid, 226801 (2005).

[2] See, for example, Jun Goryo, Nobuki Maeda, and Ken-Ichiro Imura, "Superconductivity and Current Confinement in Z2 Topological Insulator", arXiv:0905.2296

[3] K. I. Bolobin, et al, arXiv:0910.2763

[4] A. Shitade, et al, Phys. Rev. Lett. 102, 256403 (2009).

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**$B9V1i Tomio Petrosky (The University of Texas)
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The eigenvalue problem of a quantum collision operator.AN in a kinetic equation is discussed.AN for momentum relaxation processes in a molecular.AN chain,N where a vibron isN weakly coupled to a thermal phonon bath. As a consequence of a constraint due to the resonance condition, the momenta of the vibron associated through the collision operator successively with a representative momentum.AN form a subset separated from other momenta. The number of possible values of momenta in each subset and the spectrum of the collision operator crucially depend on the rationality or irrationality of the parameter $R\equiv\pi^{-1}\sin^{-1}B$, where $B$ denotes the ratio of the phonon bandwidth to the vibron bandwidth. The plot of the spectrum as a function of $R$ shows a fractal structure.AN reminiscent ofN Hofstadter's butterfly, which was found for a Hamiltonian system of a Bloch electron in two dimensions under a magnetic field. However,.AN the shape looks like a lobster or a Japanese special effects TV character, Alien Baltan, rather than butterflies.