相关论文: Energy transfer, weak resonance, and Fermi's golde…
We consider perturbations of the one-dimensional cubic Schr\"odinger equation, of the form $i \, \partial_t \psi + \partial_x^2 \psi + |\psi|^2 \psi + g( |\psi|^2 ) \psi = 0$. Under hypotheses on the function $g$ that can be easily verified…
We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state;…
We review the calculation of Fermi's golden rule for a system of $N$-body dipoles, magnetic or electric, weakly interacting with a blackbody radiation. By using the magnetic or electric field-field correlation function evaluated in the…
Topological objects resulting from symmetry breakdown may be either stable or metastable depending on the pattern of symmetry breaking. However, if they acquire zero-energy modes of fermions, and in the process acquire non-integer fermionic…
The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…
We consider a one-dimensional partial differential equation system modeling heat flow around a ring. The system includes a Klein-Gordon wave equation for a field satisfying spatial periodic boundary conditions, as well as Ornstein-Uhlenbeck…
In this analysis, we study the dynamics of quantum oscillator fields within the context of a position-dependent mass (PDM) system situated in an Einstein-Maxwell space-time, incorporating a non-zero cosmological constant. The magnetic field…
We consider nonlinear Schr\"odinger equations in $\R^3$. Assume that the linear Hamiltonians have two bound states. For certain finite codimension subset in the space of initial data, we construct solutions converging to the excited states…
A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schr\"{o}dinger equation, it preserves the total energy but not the kinetic…
Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary…
We introduce a concept of non-coherent evolution of macroscopic quantum systems. We show that for weakly interacting systems such evolution is a Markovian stochastic process. The transition rates between system states, which characterize…
We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.
The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss…
We revisit the Fermi two-atoms problem in the framework of disordered systems. In our model we consider a two-qubits system linearly coupled with a quantum massless scalar field. We analyze the energy transfer between the qubits under…
The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in…
We investigate experimentally a Fermi golden rule in two-edge and five-edge microwave networks with preserved time reversal invariance. A Fermi golden rule gives rates of decay of states obtained by perturbing embedded eigenvalues of graphs…
We study fermions at quantum criticality with extremely retarded interactions of the form $V(\omega_l)=(g/|\omega_l|)^\gamma$, where $\omega_l$ is the transferred Matsubara frequency. This system undergoes a normal-superconductor phase…
We show that the coupling of quantum emitters to a two-dimensional reservoir with a simple band structure gives rise to exotic quantum dynamics with no analogue in other scenarios and which can not be captured by standard perturbative…
We present semiclassical approximations to Green's functions of multidimensional systems, extending Gutzwiller's work to the classically forbidden region. Based on steepest-descent integrals over these functions, we derive an instanton…
We study heat transfer in one-dimensional Fermi-Pasta-Ulam-Tsingou type systems with long-range (LR) interactions. The strength of the LR interaction between two lattice sites decays as a power $\sigma$ of the inverse of their distance. We…