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The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
Even dimensional defects and boundaries in conformal field theory support type $a$ anomalies on their world-volume. We show that the one-point functions of marginal operators, in the presence of defects and boundaries, are anomalous, and…
We discuss the experimental photoemission and inverse photoemission of early transition metal oxides, in the light of the dynamical mean field theory of correlated electrons which becomes exact in the limit of infinite dimensions. We argue…
The limitations of three-dimensional semi-classical gravity are explored in the context of a conformally invariant theory for a self-interacting scalar field. The analysis of the theory's scaling behaviour reveals that scalar-loop effects…
Close to the Mott transition, lattice degrees of freedom react to the softening of electron degrees of freedom. This results in a change of lattice spacing, a diverging compressibility and a critical anomaly of the sound velocity. These…
It is demonstrated through Monte Carlo simulations that the one component lattice Coulomb gas model in two dimensions under certain conditions display features of an anomalous dynamic response. We suggest that pinning, which can either be…
The conformal anomaly has well-known ambiguities related to the possible schemes of regularization and renormalization. In case of dimensional regularization, one of the options is to formulate the theory as conformal in the dimension $D…
The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a…
Theoretical predictions and experimental discoveries for neutron-rich, short-lived nuclei far from stability indicate that the familiar concept of nucleonic shell structure should be considered as less robust than previously thought. The…
We study formation and evolution of solitons within a model with two real scalar fields with the potential having a saddle point. The set of these configurations can be split into disjoint equivalence classes. We give a simple expression…
The backreaction of structure formation influences the cosmological evolution equation for the homogenous and isotropic average metric. In a cold dark matter universe this effect leads only to small corrections unless a substantial fraction…
The constraints on the models for the structure formation arising from various cosmological observations at different length scales are reviewed. The status of different models for structure formation is examined critically in the light of…
We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed…
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we…
The present paper examines the possibility of asymmetric effect of the adjacent to barrier physically different media, or anisotropic structure of the barrier itself, on probability of the oppositely directed transitions of current carriers…
In this work the influence of the chiral anomaly effect on the evolution of magnetohydrodynamic turbulence was studied. We argue that in the early universe, before the electroweak symmetry breaking, and for temperatures high enough such…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
The anomalous scaling phenomena of three-dimensional passive scalar turbulence are studied using high resolution direct numerical simulation. The inertial range scaling exponents of the passive scalar increment and the scalar dissipation…
We discuss the phenomenological extraction of the leading $ j$-plane singularity from singlet structure functions $ F_s $ measured at small $ x. $ Using a saddle-point method we show that $ {\rm d ln} F_s /{\rm d ln}{1 \over x} $ is a…
We consider a one-dimensional Dicke lattice with complex photon hopping amplitudes and investigate the influence of time-reversal symmetry breaking due to synthetic magnetic fields. We show that, by tuning the total flux threading the…