Related papers: Nonlinear dynamics of superpostion of wavepackets
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We discuss a method by which quantum fluctuations can be included in microscopic transport models based on wave packets that are not energy eigenstates. By including the next-to-leading order term in the cumulant expansion of the…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The…
We propose a modified dynamics of quantum mechanics, in which classical mechanics of a point mass derives intrinsically in a massive limit of a single-particle model. On the premise that a position basis plays a special role in wavefunction…
With the exception of the harmonic oscillator, quantum wave-packets usually spread as time evolves. We show here that, using the nonlinear resonance between an internal frequency of a system and an external periodic driving, it is possible…
The exploration of new problem classes for quantum computation is an active area of research. In this paper, we introduce and solve a novel problem class related to dynamics on large-scale networks relevant to neurobiology and machine…
In this work it is shown that there is an inherent nonlinear evolution in the dynamics of the so-called generalized coherent states. To show this, the immersion of a classical manifold into the Hilbert space of quantum mechanics is…
In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact…
We study the energy redistribution of interacting bosons in a ring-shaped quantum trimer as the coupling strength between neighboring sites of the corresponding Bose-Hubbard Hamiltonian undergoes a sudden change dk. Our analysis is based on…
We study the dynamics of quantum statistical ensembles at first-order phase transition points of finite macroscopic systems. First, we show that at the first-order phase transition point of systems with an order parameter that does not…
While the linearity of the Schr\"odinger equation and the superposition principle are fundamental to quantum mechanics, so are the backaction of measurements and the resulting nonlinearity. It is remarkable, therefore, that the…
We investigate the dynamics of overdamped $D$-dimensional systems of particles repulsively interacting through short-ranged power-law potentials, $V(r)\sim r^{-\lambda}\;(\lambda/D>1)$. We show that such systems obey a non-linear diffusion…
The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…
We derive the theory of open quantum system dynamics intervened by a series of nonselective measurements. We analyze the cases of time independent and time dependent Hamiltonian dynamics in between the measurements and find the approximate…
The nonlinear dynamics of dissipative quantum systems in incoherent laser fields is studied in the framework of master equation with random model describing the laser noise and Markovian approximation for dealing with the system-bath…
The Hamiltonian dynamics of chains of nonlinearly coupled particles is numerically investigated in two and three dimensions. Simple, off-lattice homopolymer models are used to represent the interparticle potentials. Time averages of…
Understanding complex quantum dynamics in realistic materials requires insight into the underlying correlations dominating the interactions between the participating particles. Due to the wealth of information involved in these processes,…
Quantum mechanics allows coherent superposition between different states of matter. This quality is responsible for major non-classical phenomena that occur in quantum systems. Beyond states, coherent superpositions are also possible…
We present here a set of lecture notes on quantum systems with time-dependent boundaries. In particular, we analyze the dynamics of a non-relativistic particle in a bounded domain of physical space, when the boundaries are moving or…