Related papers: An inverse problem for data-driven prediction in q…
Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
We compute the survival probability of an initial state, with an energy in a certain window, by means of random matrix theory. We determine its probability distribution and show that is is universal, i.e. caracterised only by the symmetry…
We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and…
Reconstructing a quantum system's Hamiltonian from limited yet experimentally observable information is interesting both as a practical task and from a fundamental standpoint. We pose and investigate the inverse problem of reconstructing a…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown.…
We show how to derive fixed-point Hamiltonians in quantum mechanics from a proposed renormalization group invariance approach that relies in a subtraction procedure at a given energy scale. The scheme is valid for arbitrary interactions…
A new class of random quantum--dynamical systems in continuous space is introduced and studied in some detail. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic,…
The inverse Henderson problem of statistical mechanics concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles. Roughly stated, it asks for the interaction…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the…
We consider physical Hamiltonians that can be represented by the multiparametric Gaussian ensembles, theoretically derive the state ensembles for its eigenstates and analyze the effect of varying system conditions on its bipartite…
The universal quantum work relation connects a functional of an arbitrary observable averaged over the forward process to the free energy difference and another functional averaged over the time-reversed process. Here, we ask the question…
In the previous paper, it has been proved that elastic scattering processes of two quantum particles are always accompanied with nonlocal processes. Furthermore, it is found that setting an additional Hamiltonian after the originally…
The range of a quantum measurement is the set of outcome probability distributions that can be produced by varying the input state. We introduce data-driven inference as a protocol that, given a set of experimental data as a collection of…
Perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. An effective Hamiltonian that is accurate to second order in the inverse heavy mass is derived. It contains a new…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a…