Related papers: Lagrangian versus Quantization
The paper reviews various arithmetic analogues of Hamiltonian systems and presents some new facts suggesting ways to relate/unify these examples.
In this paper, we try to generalise quantum stabilizer formalism to any composite system, that is, it includes not only composite systems of equal dimensions, but also composite systems of unequal dimensions.
A geometric description is given for the Sp(2) covariant version of the field-antifield quantization of general constrained systems in the Lagrangian formalism. We develop differential geometry on manifolds in which a basic set of…
A membrane technique, in which the symplectic and Ricci forms are integrated over surfaces in a complexification of the phase space, as well a ``creation" connection with zero curvature over lagrangian submanifolds, is used to obtain a…
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought…
The quantum Zakharov system is described in terms of a Lagrangian formalism. A time-dependent Gaussian trial function approach for the envelope electric field and the low-frequency part of the density fluctuation leads to a coupled,…
Quantum metrology based on quantum entanglement and quantum coherence improves the accuracy of measurement. In this paper, we briefly review the schemes of quantum metrology in various complex systems, including non-Markovian noise,…
In order to derive a large set of Hamiltonian dynamical systems, but with only first order Lagrangian, we resort to the formulation in terms of Lagrange-Souriau 2-form formalism. A wide class of systems derived in different phenomenological…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
The biological hierarchy and the differences between living and non-living systems are considered from the standpoint of quantum mechanics. The hierarchical organization of biological systems requires hierarchical organization of quantum…
Although the suspicion that quantum mechanics is emergent has been lingering for a long time, only now we begin to understand how a bridge between classical and quantum mechanics might be squared with Bell's inequalities and other…
We propose a method to design a suboptimal, coherent quantum LQG controller to solve a quantum equalization problem. Our method involves reformulating the problem as a control problem and then designing a classical LQG controller and…
We explore the sense in which the state of a physical system may or may not be regarded (an) observable in quantum mechanics. Simple and general arguments from various lines of approach are reviewed which demonstrate the following no-go…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…
We describe a method to axiomatize computations in deterministic Turing machines. When applied to computations in non-deterministic Turing machines, this method may produce contradictory (and therefore trivial) theories, considering…
An analysis using classical stochastic processes is used to construct a consistent system of quantum counterfactual reasoning. When applied to a counterfactual version of Hardy's paradox, it shows that the probabilistic character of quantum…
Lagrangian relaxation has been used extensively in the design of approximation algorithms. This paper studies its strengths and limitations when applied to Partial Cover.
I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the "naive" quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether…
The characterization of quantum correlations is crucial to the development of new quantum technologies and to understand how dramatically quantum theory departs from classical physics. Here we systematically study single- and multiparticle…