Self-Organizing Systems

TLDR: This chapter describes the efforts of cosmologists (and nature?) to form galactic and stellar structures, comments on them from the viewpoint of the homeokinetic principles, and pursues some parallels in the origin of life.

Abstract: 1 This chapter shows application of a consistent set of clear physical principles to describe the beginnings of the universe by the (hot) Big Bang model. The ultimate beginning presents difficulties for the physicist, particularly when it comes to explaining why we find a very inhomogeneous cosmos, instead of a uniform, radiating gas. Stars, globular clusters, galaxies, and clusters of galaxies dot space, but we cannot at present explain their presence without invoking a "deus ex machina." We expect ultimately to rationalize the existence of these local inhomogeneities through gravitational contractions of regions of higher than average mass density that in tum arise out of fluctuations, but the case cannot yet be made completely. Meanwhile, the Big Bang (incomplete) model deals with cosmic evolution in the large, as a balance between gravitational attraction and cosmic expansion. Its relationships are described by two simple equations derived from Einstein's theory of general relativity via local conservations of mass-energy and of momentum. Unfortunately, this model does not by itself produce the observed inhomogeneities. Neither the assumption of thermodynamic fluctuations following a "smooth" beginning nor that ofa chaotic beginning can itself account for stars and galaxies. A mystery remains. -THE EDITOR This chapter describes the efforts of cosmologists (and nature?) to form galactic and stellar structures, comments on them from the viewpoint of the homeokinetic principles (Soodak and Iberall, 1978) discussed elsewhere in this volume, and pursues some parallels in the origin of life. It appears that there are no serious problems in understanding the origin of stars, given the previous formation of a galactic gas mass. A number of reasonable, even likely, paths lead to star formation. On the other hand, the origin of inhomogeneities required to initiate galaxy formation is not yet known. Appendix 1 remarks on some advances in observational and theoretical cosmology made since the original writing of this chapter HARRY SOODAK • Department of Physics, The City College of New York, New York, New York

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Naraˇsˇcanje energije v ˇcasovno odvisnih biljardnih
sistemih
BENJAMIN BATISTI
´
C
CAMTP - Center for Applied Mathematics and Theoretical Physics
University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
benjamin.batistic@uni-mb.si • www.camtp.uni-mb.si
Energija ˇcasovno odvisnih sistemov se ne ohranja . Zanima nas pod kakˇsnimi sploˇsnimi
pogoji lahko energija ˇcasovno odvisnega sistema neomejeno naraˇsˇca.
ˇ
Casovno odvisni biljardi sluˇzijo kot preprosti modeli sploˇsnejˇsih ˇcasovno odvisnih
sitemov , ki so zelo prikla d ni za numer iˇcno raˇcunanje. Numeriˇcni raˇcuni s ˇcasovno
odvisnimi b i l jar d i v sploˇsn em kaˇzejo, da povpreˇcna hitrost ansambla, po velikem
ˇstevilu tr kov, sledi potenˇcnemu zako nu v ∝ n
β
, kjer je n ˇstevilo trkov. Vrednost
parametra β varira n a intervalu med 0 in 1 in je odvisna od din a m iˇcnih lastn o st i
zamrznjenega biljarda in od naˇcin a dihanja. V primeru popolnoma kaotiˇcnih b i l -
jardov vidimo, da lahko ima β zgolj eno od treh vrednosti β = 1/6, 1/4, 1/2 [1,2],
medtem ko je v sistemih meˇsanega tipa slika precej bolj zapletena [3,4].
Reference
[1] B. Batisti´c and M. Robnik, J. Phys. A: Math. Theor. 44 (2011) , 365101
[2] B. Batisti´c and M. Robnik, in 8th Inter n at i on al Su m m er Schoo l /Co n fer en c e
“Let’s Face Chaos throug h Nonlinear Dynaimcs”, Eds. M. Robnik and V.
Romanov sk i , AIP conf. proc. 1469 (2012), 27
[3] F.Lenz, F. K. Di a konos and P. Schmelcher, PRL 100 (2008), 014103
[4] E. D. Leonel, D. F. M. Oliveira and A. Loskutov, Chaos 19 (2009), 033142

The energy growth in time-dependent billiard
systems
BENJAMIN BATISTI
´
C
CAMTP - Center for Applied Mathematics and Theoretical Physics
University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
benjamin.batistic@gmail.com • www.camtp.uni-mb.si
Energy of a ti m e- d ependent system is not conserved. The question is under which
general conditions th e energy of a ti m e- d ependent system grows infinitely.
Time-dependent billiards serve as simple models of general time-dependent systems,
which are very suitable for numerical computations. Numerical calculations with
time-dependent bi l l i a r d s in general show that the ave ra g e velocity v of an ensembl e,
after a large number of collisions, follows the power law v ∝ n
β
, where n denotes
the number of collisions. The value of the acceleration exponent β is rest r i ct ed to
the inter val between 0 and 1 and depends on the dynamical properties of the frozen
billiard as well as on the driving law. In the case of the fully chaotic time-dependent
billiards the exponent β can be only one of three values 1/6, 1/4, 1/2 [1,2]. However,
for the mixed type systems the pic tu r e is far more comp l i ca t ed [3,4].
References
[1] B. Batisti´c and M. Robnik, J. Phys. A: Math. Theor. 44 (2011), 365101
[2] B. Batisti´c and M. Robnik, in 8th Inter n at i on al Su m m er Schoo l /Co n fer en c e
“Let’s Face Chaos throug h Nonlinear Dynaimcs”, Eds. M. Robnik and V.
Romanov sk i , AIP conf. proc. 1469 (2012), 27
[3] F.Lenz, F. K. Di a konos and P. Schmelcher, PRL 100 (2008), 014103
[4] E. D. Leonel, D. F. M. Oliveira an d A. Loskutov, Chaos 19 (2009), 033142

Neravnovesna dinamika veˇc-delˇcnih sistemov
JANEZ BON
ˇ
CA
Fakulteta za matematiko in fiziko, Univerza v Ljubljani, SI-1000
Ljubljana, Slovenija
Institut J. Stefan , SI -1000 Ljubljana, Slovenija
janez.bonca@ijs.si • www-f1.ijs.si
Predstav i l bom fundamentalno ˇstudijo ene in dveh vrzeli v t-J-Holsteinovem mod-
elu pod vplivom zunan jeg a elektriˇcne ga polja. Ob upoˇstevanju kvantno mehanske
narave problema sledimo ˇcasovnemu razvoju sistema zaˇcenˇsi z osnovnim stanjem ko
vkljuˇcim o elektriˇcno polje ob ˇcasu niˇc ter v se do stacionarnega stanja. V primeru
ene vrzeli opazimo ad i a b at sk i reˇzim, kateremu sledi reˇzim linearne I − V karakteris-
tike pri v m es n ih el ek t r iˇcnih poljih [1,2]. Pri visokih poljih se sist em n a h aja v reˇzimu
negativne difere n ci aln e upornosti. Vezan par vrzeli (bi polaron) pod vp l i vom elek-
triˇcnega polja razpade na dva neodvisna spinska polarona [3]. Odkrili smo razliˇcna
univer za l n a obnaˇsanja sistema pri majhnih ter velikih ˇcasih merjenih od vkljuˇcitve
zunanjega elek tr iˇcnega polja. Raziskal bom tudi relaksacijo s kratki m elektriˇcnim
pulzom vzbujenega Hoslt ei n ovega polarona [4].
References
[1] M. Mierzejewski, L. Vidmar, J. Bonˇca, and P. Prelovˇsek, Phys. Rev. Lett.
106 196401, (2011).
[2] L. Vidm a r, J. Bonˇca, T. Tohyama, and S. Maekawa, Phys. Rev. Lett. 107
246404, (2011).
[3] J. Bonˇca, M. Mierzejewski, and L. Vidmar, Phys. Rev. Lett. 109 156404,
(2012).
[4] D. Goleˇz, J. Bonˇca, L. Vi d m a r , and S. A. Trugman, to appear in Phys. Rev.
Lett. (2012).

Nonequilibrium dynamics of many-body systems
JANEZ BON
ˇ
CA
Faculty of Mathematics and Physics, University of Ljubljana,
SI-1000 Ljubljana, Slovenia
J. Stefan Institute, SI-1000 Ljubljana, Slovenia
janez.bonca@ijs.si • www-f1.ijs.si
I will present a fundamental stud y of one and two holes in the two dimensional t-J-
Holstein model dri ven by th e electric field. Taking fully into account quantum effects
we follow the time-evolution of systems from their ground state as th e electric field is
switched on at t = 0, until they reach a steady state. In the single hole ca se adiabatic
regime is observed followed by the positive different i a l resistivity at moderate field s
where carrier mobility is det er mi n ed [1, 2] . At large field the system enters negative
different i a l resistivity regime where current remains finite, p ro portional to 1/F . I
will also discuss the dissociation of a bound hole pair (bip ol a r on ) under the influence
of the external electric field [ 3 ] . Different universal behaviors are observed at short as
well as long times after switching on the electric field. I will also present relaxation
dynamics of a Ho l st ei n polaron after the excitation by a sh o r t electric pulse [4].
References
[1] M. Mierzejewski, L. Vidmar, J. Bonˇca, and P. Prelovˇsek, Phys. Rev. Lett.
106 196401, (2011).
[2] L. Vidm a r, J. Bonˇca, T. Tohyama, and S. Maekawa, Phys. Rev. Lett. 107
246404, (2011).
[3] J. Bonˇca, M. Mierzejewski, and L. Vidmar, Phys. Rev. Lett. 109 156404,
(2012).
[4] D. Goleˇz, J. Bonˇca, L. Vi d m a r , and S. A. Trugman, to appear in Phys. Rev.
Lett. (2012).

Kompleksne faze v plastno urejenih tekoˇcih
kristalih
MOJCA
ˇ
CEPI
ˇ
C
Pedagoˇska fakulteta
Univerza v Ljubljani, Kardeljeva pl. 16, SI-1000 Ljubljana, Slovenia
in
Institut Joˇzef Stefan
Jamova 39, SI-1000 Ljubljana, Slovenia
mojca.cepic@pef.uni-lj.si • www.pef.uni-lj.si
Tekoˇci kristali so snovi, ki imajo med trdno in tekoˇco fazo ˇse vsaj eno fazo z
lastnostmi kristalov in te koˇcin hkrati. Strukture tekoˇce kristalnih faz so komp l ek-
sne, saj se moduliranost orientacijskega reda lahko prepleta s kom p l e ks n i m i pozi-
cijskimi redi. Prispevek je omejen na tekoˇce kristale, ki tvorijo plastne strukture.
Opisala bom strukture nekaterih kompleksni h faz in predstavila njihov zvezni teo-
retiˇcni opis. Zvezni teoretiˇcni model ne more razloˇziti vzrokov za n ast a n ek vseh
faz. Diskretiza ci ja zveznega modela p a ta problem razreˇsi. V diskretnem modelu
se interakcije med molek u l am i delijo na interakcije med molekulami v plasti in med
molekulami razliˇcnih plasti. Kadar imajo int er akcije med razliˇcnimi plastmi naspro-
tujoˇce si uˇcinke, postanejo stabilne faze s kompl e ks n i m i strukturami, katerih periode
se lahko raztezajo preko mnogih plasti. V okvi r u diskretnega modela je bilo mogoˇce
napovedati strukture nekaterih faz, ki so bile kasneje tudi eksperimentalno potrjene.
Reference
[1] H. Takezoe, E. Gorecka, M.
ˇ
Cepiˇc, Reviews of Modern Physics 82 (2010) 897-
937.