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Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an…
In the past decade, the toolkit of quantum information has been expanded to include processes in which the basic operations do not have definite causal relations. Originally considered in the context of the unification of quantum mechanics…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
Recently there has been a claim on the complete irrelevance of quantum modeling for plasmas. We address this subject from basic principles. Physical situations where quantum effects play a decisive role are identified.
The general conditions under which the quadratic, uniform and monotonic convergence in the quasilinearization method of solving nonlinear ordinary differential equations could be proved are formulated and elaborated. The generalization of…
We present exact quantum solutions for a noncommutative, multidimensional cosmological model and show that stabilization of extra dimensions sets in with the introduction of noncommutativity between the scale factors. An interpretation is…
It is shown that any dynamic equation on a configuration bundle $Q\to R$ of non-relativistic time-dependent mechanics is associated with connections on the affine jet bundle $J^1Q\to Q$ and on the tangent bundle $TQ\to Q$. As a consequence,…
We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation…
We study the behaviour of a nonrelativistic quantum particle interacting with different potentials in the spacetimes of topological defects. We find the energy spectra and show how they differ from their free-space values.
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V.…
Motivated by issues in the context of asymptotically flat spacetimes at null infinity, we discuss in the simplest example of a massless scalar field in two dimensions several subtleties that arise when setting up the canonical formulation…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
We investigate whether non-positive operator-valued measurements can be beneficial for quantum metrology. For unitary encoding, we show that non-positive measurements offer no advantage over positive ones. Going over to open encoding, we…
Non-relativistic string theories promise to provide simpler theories of quantum gravity as well as tractable limits of the AdS/CFT correspondence. However, several apparently distinct non-relativistic string theories have been constructed.…
This article defines and proves basic properties of the standard quantum circuit model of computation. The model is developed abstractly in close analogy with (classical) deterministic and probabilistic circuits, without recourse to any…
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
Reciprocal transformations mix the role of the dependent and independent variables to achieve simpler versions or even linearized versions of nonlinear PDEs. These transformations help in the identification of a plethora of PDEs available…
We consider Noncommutative Quantum Mechanics with phase space noncommutativity. In particular, we show that a scaling of variables leaves the noncommutative algebra invariant, so that only the self-consistent effective parameters of the…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…