Related papers: The Conditional Probability Interpretation of the …
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…
Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical…
This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…
If a coupling between the inflaton and the Gauss-Bonnet term is introduced, many models of inflation that were ruled out by the most recent Planck data can be made viable again. The predictions for the scalar spectral index and…
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. A quantum theory of closed systems requires two elements; 1) a condition specifying which sets of histories may…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
In quantum field theory, Hamiltonians contain particle creation and annihilation terms that are usually ultraviolet (UV) divergent. It is well known that these divergences can sometimes be removed by adding counter-terms and taking limits…
Observables and instruments have played significant roles in recent studies on the foundations of quantum mechanics. Sequential products of effects and conditioned observables have also been introduced. After an introduction in Section~1,…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We consider the use of quantum error detecting codes, together with energy penalties against leaving the codespace, as a method for suppressing environmentally induced errors in Hamiltonian based quantum computation. This method was…
In this paper, we propose a generalized successive approximation method (SAM), called invariantly admissible policy iteration (PI), for finding the solution to a class of input-affine nonlinear optimal control problems by iterations. Unlike…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
Path integrals are usually formulated in discrete Euclidean time using the Trotter formula. We propose a new method to study discrete quantum systems, in which we work directly in the Euclidean time continuum. The method is of general…
Quantum computing promises exponential improvements in solving large systems of partial differential equations (PDE), which forms a bottleneck in high-resolution computational fluid dynamics (CFD) simulations, in, among others, aerospace…
The Vanilla Power Law Inflation is plagued with two severe drawbacks, the one being the issue of graceful exit, and the other being its compatibility with the existing data. There's yet another daunting problem generic to any inflationary…
We introduce the concept of quantum polymorphisms to the complexity theory of quantum constraint satisfaction. Via this notion, we build an algebraic framework of reductions between quantum CSPs, and we establish a Galois connection between…
The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…