Related papers: Quantum Simulation of Non-Unitary Dynamics via Amp…
The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…
We investigate the dynamics of a quantum system coupled linearly to Gaussian white noise using functional methods. By performing the integration over the noisy field in the evolution operator, we get an equivalent non-Hermitian Hamiltonian,…
Phase modulation has scarcely been mentioned in diffusive systems since the diffusion process does not carry momentum like waves. Recently, the non-Hermitian physics provides a new perspective for understanding diffusion and shows prospects…
Non-Hermitian Hamiltonians provide a simple picture for inspecting dissipative systems with natural or induced gain and loss. We investigate the Floquet dynamical phase transition in the dissipative periodically time driven XY and extended…
Mean-field characterizations of first-order iterative algorithms -- including Approximate Message Passing (AMP), stochastic and proximal gradient descent, and Langevin diffusions -- have enabled a precise understanding of learning dynamics…
Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation expansion for general dissipative partial…
A decomposition principle for nonlinear dynamic compartmental systems is introduced in the present paper. This theory is based on the mutually exclusive and exhaustive, analytical and dynamic, novel system and subsystem partitioning…
We study the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing non-unitary dynamic properties. The interplay of interactions and non-hermiticity results in…
Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have aided multiple fields including chemistry, biology and physics. However, accurate quantum dynamical simulations based on model…
Non-Hermitian physics has emerged as a rich field of study, with applications ranging from $PT$-symmetry breaking and skin effects to non-Hermitian topological phase transitions. Yet most studies remain restricted to small-scale or…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
We consider the dissipative dynamics of a qubit coupled to a nonlinear oscillator (NO) embedded in an Ohmic environment. By treating the nonlinearity up to first order and applying Van Vleck perturbation theory up to second order in the…
Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their…
We propose a novel Augmented Mass-Spring (AMS) model for real-time simulation of dense hair at strand level. Our approach considers the traditional edge, bending, and torsional degrees of freedom in mass-spring systems, but incorporates an…
Over the past decade classical optical systems with gain or loss, modelled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic…
We introduce a novel non-equilibrium phase -- the quantum many-body scar (QMBS) phase -- that emerges in non-Hermitian many-body dynamics when scarred wavefunctions are selectively stabilized via non-Hermitian driving. Projective…
Non-Hermitian physics has emerged as a rapidly advancing field of research, revealing a range of novel phenomena and potential applications. Traditional non-Hermitian Hamiltonians are typically simulated by constructing asymmetric couplings…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…