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The simulation of quantum processes is a key goal for the grand programme aiming at grounding quantum technologies as the way to explore complex phenomena that are inaccessible through standard, classical calculators. Some interesting steps…
The existence of solutions to Tolman-Openheimer-Volkoff equation with linear equation of state modeling relativistic cloud of interacting particles is proved for mass parameter below certain threshold. For the intermediate values of mass…
Full information about a many-body quantum system is usually out-of-reach due to the exponential growth -- with the size of the system -- of the number of parameters needed to encode its state. Nonetheless, in order to understand the…
Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of…
We consider a lattice of weakly interacting quantum Markov processes. Without interaction, the dynamics at each site is relaxing exponentially to a unique stationary state. With interaction, we show that there remains a unique stationary…
The desire to produce high-quality single photons for applications in quantum information science has lead to renewed interest in exploring solid-state emitters in the weak excitation regime. Under these conditions it is expected that…
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…
We give an elementary proof of positivity of total gravitational energy in space-times containing complete smooth light-cones.
We study the existence and stability of standing waves for a system of nonlinear Schr\"odinger equations with quadratic interaction in dimensions $d\leq 3$. We also study the characterization of finite time blow-up solutions with minimal…
We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum…
We prove the existence of an infinite family of smooth positive bound states for (N +1)-coupled long-wave--short-wave interaction equations. The system describes the interaction between N short waves and a long wave and is of interest in…
We consider the Lane-Emden system $-\Delta u = v^p$, $-\Delta v= u^\theta$ in $\mathbb{R}^N$, and we prove the nonexistence of smooth positive solutions which are stable outside a compact set, for any $p, \theta > 0$ under the Sobolev…
Scalable quantum computation with linear optics was considered to be impossible due to the lack of efficient two-qubit logic gates, despite its ease of implementation of one-qubit gates. Two-qubit gates necessarily need a nonlinear…
As a key index for applications of a device, the device's reliability is its ability to survive (function normally over time) under the influence of some environment. In this paper we present a quantum energy-storing device model with a…
We prove the existence of limiting distributions for a large class of Markov chains on a general state space in a random environment. We assume suitable versions of the standard drift and minorization conditions. In particular, the system…
The study of non-equilibrium physics from the perspective of the quantum limits of thermodynamics and fluctuation relations can be experimentally addressed with linear optical systems. We discuss recent experimental investigations in this…
We formulate an exact spacetime mapping between the $\mathcal{N}$-point correlation functions of two different experiments with open quantum gases. Our formalism extends a quantum-field mapping result for closed systems [Phys. Rev. A…
We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce…
We study the asymptotic behaviors of solutions of the Loewner-Nirenberg problem in singular domains and prove that the solutions are well approximated by the corresponding solutions in tangent cones at singular points on the boundary. The…
The effect of long-ranged Coulomb interaction on the low energy properties (momentum distribution function, density of states, electron spectral function, and $4k_F$ correlation function) of one-dimensional electron systems is determined…