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The magnetic susceptibility of an ensemble of clean metallic nanoparticles is shown to change from paramagnetic to diamagnetic one with the onset of spin-orbit interaction. The effect is quantified on the basis of symmetry analysis with the…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
A new statistical ensemble is examined using the example of classical one-component simple fluid. It's logical to call it an open ensemble, because its peculiarity is the inclusion in the consideration some surrounding area. Calculations…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
A system of two initially homogeneous, physically real fields uniformly attracted to each other is considered as the simplest basis of the self-developing world structure. It is shown that the system is unstable against periodic cycles of…
Symmetry is at the heart of much of mathematics, physics, and art. Traditional geometric symmetry groups are defined in terms of isometries of the ambient space of a shape or pattern. If we slightly generalize this notion to allow the…
The free energy landscape of mean field marginal glasses is ultrametric. We demonstrate that this feature remains in finite three dimensional systems by finding sets of minima which are nearby in configuration space. By calculating the…
We construct rather general random ensembles that yield the optimal (isomorphic) estimate in the Dvoretzky-Milman Theorem. This is the first construction of non gaussian/spherical ensembles that exhibit the optimal behaviour. The ensembles…
The visible band (band A) of Photoluminescence spectra of high-purity synthesized diamond is analyzed by deconvolution technique. A set of eight lines with distinct peak energy are found. The peak energy and the width of these lines were…
Spherical Designs are finite sets of points on the sphere $\mathbb{S}^{d}$ with the property that the average of certain (low-degree) polynomials in these points coincides with the global average of the polynomial on $\mathbb{S}^{d}$. They…
Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…
The notion of $p$-modulus of a family of objects on a graph is a measure of the richness of such families. We develop the notion of minimal subfamilies using the method of Lagrangian duality for $p$-modulus. We show that minimal subfamilies…
We have located the global minimum for all lead clusters with up to 160 atoms using a glue potential to model the interatomic interactions. The lowest-energy structures are not face-centred cubic as suggested previously. Rather, for N<40…
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal measures are discrete or are supported on small sets. In…
The optical properties of clusters with metallic spherical particles embedded in an insulating matrix are studied. A theoretical approach is proposed for the calculation of the macroscopic dielectric response for a collection of spheres at…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…
An `open' or $(\mu,P,T)$-ensemble describes equilibrium systems whose control parameters are chemical potential $\mu$, pressure $P$ and temperature $T$. Such an unconstrained ensemble is seldom used for applications to standard…
We calculate the magnetic response of ensembles of small two-dimensional structures at finite temperatures. Using semiclassical methods and numerical calculation we demonstrate that only short classical trajectories are relevant. The…
A discrete set in the Euclidian space is almost periodic, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We prove the following result: if A is a discrete almost periodic set and the set A-A…
$L$-ensembles are a class of determinantal point processes which can be viewed as a statistical mechanical systems in the grand canonical ensemble. Circulant $L$-ensembles are the subclass which are locally translationally invariant and…