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Noncommutative phase space of an arbitrary dimension is considered. The both of operators coordinates and momenta in noncommutative phase space may be noncommutative. In this paper, we introduce momentum-momentum noncommutativity in…
We study a system of non-identical bistable particles that is driven by a dynamical constraint and coupled through a non-local mean-field. Assuming piecewise affine constitutive laws we prove the existence of traveling wave solutions and…
We study a class of models of i.i.d.~random environments in general dimensions $d\ge 2$, where each site is equipped randomly with an environment, and a parameter $p$ governs the frequency of certain environments that can act as a barrier.…
A new kind of aperiodic tiling is introduced. It is shown to underlie a structure obtained as a superposition of waves with incommensurate periods. Its connections to other other tilings and quasicrystals are discussed.
Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple…
We obtain the exact expression for the matrix of nonadiabatic transition probabilities in the model of three interacting states with a time-dependent Hamiltonian. Unlike other known solvable Landau-Zener-like problems, our solution is…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
The Rosenzweig-Porter model is a one-parameter family of random matrices with three different phases: ergodic, extended non-ergodic and localized. We characterize numerically each of these phases and the transitions between them. We focus…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
The study of critical phenomena and phase transitions is an important part of modern condensed matter physics. In this regard, the phenomenological Landau theory has been extraordinarily useful. Hereby we present an alternative theoretical…
The discovery of topological phases of matter and topological boundary states had tremendous impact on condensed matter physics and photonics, where topological phases are defined via energy bands, giving rise to topological band theory.…
We study fluctuating field models with spontaneously emerging dynamical phases. We consider two typical transition scenarios associated with parity-time symmetry breaking: oscillatory instabilities and critical exceptional points. An…
We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica…
We investigate a two-dimensional tiling model. Even though the degrees of freedom in this model are discrete, it has a hidden continuous global symmetry in the infinite lattice limit, whose corresponding Goldstone modes are the…
Analytically solvable models are benchmarks in studies of phase transitions and pattern-forming bifurcations. Such models are known for phase transitions of the second kind in uniform media, but not for localized states (solitons), as…
Nonadiabatic dressed states of a quantum system interacting with an external electromagnetic field and the environment are presented. The relevant matrix elements within the specified states are found. A closed form expression of the…
The realization of a genuine phase transition in quantum mechanics requires that at least one of the Kato's exceptional-point parameters becomes real. A new family of finite-dimensional and time-parametrized quantum-lattice models with such…
Majorana bound states are interesting candidates for applications in topological quantum computation. Low energy models allowing to grasp their properties are hence conceptually important. The usual scenario in these models is that two…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on $T^2$ and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange…