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The research herein studies the Langevin dynamics allowing for an exchange of energy between liquid crystals and the thermal environment. This dynamics leads to fluctuation and dissipation behaviors in the motions of liquid crystals, and…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
We consider a 2 d.o.f. Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. The ratio of the time derivatives of slow and fast variables is of order $0<\eps \ll 1$. At frozen…
The three-body Lennard-Jones system on the plane has a transition state, which is the straight conformation located at a saddle point of the potential energy landscape. We show that the transition state can be dynamically stabilized by…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
We study transport dynamics of ultracold cesium atoms in a two-dimensional optical lattice across the superfluid-Mott insulator transition based on in situ imaging. Inducing the phase transition with a lattice ramping routine expected to be…
A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
Many-body localization is shown to suppress imaginary parts of complex eigenenergies for general non-Hermitian Hamiltonians having time-reversal symmetry. We demonstrate that a real-complex transition, which we conjecture occurs upon…
Superclimbing dynamics is the signature feature of transverse quantum fluids describing wide superfluid one-dimensional interfaces and/or edges with negligible Peierls barrier. Using Lagrangian formalism, we show how the essence of the…
This study comprehensively investigates fast ion-driven drift instability, extending the theory in [B. J. Kang and T. S. Hahm, Phys. Plasmas 26, 042501 (2019)]. The eigenmode equation, including the resonant contribution of passing fast…
We study the relaxation mechanism of a highly excited carrier propagating in the antiferromagnetic background modeled by the $t$-$J$ Hamiltonian on a square lattice. We show that the relaxation consists of two distinct stages. The initial…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Density-matrix topology, defined through the geometric property of the relevant modular Hamiltonian, can undergo transitions in the corresponding open-system dynamics. While symmetry considerations are crucial to ensure such a dynamic…
Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. On the other hand, it is known that in slow-fast systems ergodicity of the fast sub- system impedes the equilibration of the whole…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
Searching for Anderson localization of light in three dimensions has challenged experimental and theoretical research for the last decades. Here the problem is analyzed through large scale numerical simulations, using a radiative…
Based on an attractive $U$ Hubbard model on a lattice with up to second neighbor hopping we derive an effective Hamiltonian for phase fluctuations. The superconducting gap is assumed to have s-wave symmetry. The effective Hamiltonian we…
It is shown that a lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any ''visible cause''. In such a jump the system changes instantaneously…