arXiv subjects

Yu. S. Volkov

Publications and source records attributed to Yu. S. Volkov.

5 recordsLinked to original sources

arXiv2026

Real Matrix Representations of Quantum Operators: An Introduction to Quantum Index Algebra

We introduce Quantum Index Algebra (QIA) as a finite, index-based algebraic framework for representing and manipulating quantum operators on Hilbert spaces of dimension $2^m$. In QIA, operators are expressed as structured combinations of basis elements indexed by Boolean codes, allowing products, commutators, and conjugations to be computed through finite rules on discrete indices rather than through dense matrix arithmetic. This representation unifies combinatorial index structure, explicit matrix realization, and transformation properties under Walsh-Hadamard-type transforms within a single formalism. Using QIA and its associated block-matrix realization, we reformulate the Bernstein-Vazirani hidden-string problem in its phase-oracle form entirely within a real, finite-dimensional algebraic setting. We show that, under structured oracle access, the QIA procedure reproduces the Bernstein-Vazirani algorithm exactly and achieves the same asymptotic query complexity and circuit depth as the standard quantum algorithm. In particular, the hidden string is recovered by symbolic manipulation of a sparse algebraic representation of the oracle rather than by numerical simulation of quantum amplitudes. Our results demonstrate that the apparent quantum speed-up in this setting is a consequence of operator structure rather than Hilbert-space dimensionality alone. QIA thus provides a precise language for separating genuinely quantum resources from those arising from algebraic and combinatorial structures and offers a new perspective on the classical simulability of structured quantum circuits.

quant-ph↗

arXiv2008

Pyrophosphate Groups in Liquid Crystalline Phases of the DNA

We study electrostatic interaction between molecules of the DNA in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential $U$ of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of potential $U$ indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by potential $U$. The symmetries form a noncommutative group of 8-th order, ${\cal S}$. Using the group ${\cal S}$ we suggest a classification of liquid crystalline phases of the DNA, which allows of several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the part played by charges in its liquid crystalline phases, and make for experimental research, important for nano-technological and bio-medical applications.

cond-mat.soft↗

arXiv2005

Chaotic Tunneling in a Laser Field

We study the driven tunneling of a one-dimensional charged particle confined to a rectangular double-well. The numerical simulation of the Schrödinger equation based on the Cranck-Nicholson finite-difference scheme, shows that the modulation of the amplitude of the external field may result in the parametric resonance. The latter is accompanied by the breakdown of the quasi-periodic motion characteristic of the usual driven tunneling, and the emergence of an irregular dynamics. We describe the above breakdown with the occupation probability for the ground state of the unperturbed system, and make the visualization of the irregular dynamics with the help of Shaw-Takens' reconstruction of the state-space. Both approaches agree as to the values of the resonant frequency for the parametric excitation. Our results indicate that the shape of the laser pulse could be essential for generating chaotic tunneling.

quant-ph↗

arXiv2001

Tautomeric Transitions in DNA

We study the tautomeric transitions in base pairs of DNA considering elastic properties of DNA as classical and tunneling of protons as quantum, and show that the dynamics of the transitions admits of soliton like solutions whose shape and size strongly depend on the structure of the double helix. In particular, we have found that the set of discrete breathers can be drastically modified by the interplay of the torsional and elastic constants. Our results may have a bearing upon substitution mutagenesis within the framework of Watson-Crick's approach, and in this respect the breather soliton could describe conformations corresponding to point mutations. The numerical simulation of soliton dynamics suggests that an initial distribution of base pairs with low probability of mutation per pair but of a sufficiently large number of base pairs involved, could move and gather around a site so as to form a set of base pairs with high probability of mutation, for a period of time approximately 1 musec. We suggest that the irradiation of DNA at frequencies of the proton tunneling, that is in infra-red region, could cause mutations.

cond-mat.soft↗

arXiv2000

Novel Cholesteric Phase in Dispersions of Nucleic Acids due to Polymeric Chelate Bridges

We consider cholesteric liquid-crystalline DNA dispersions, and show that polymeric (Dau-Cu) complexes, the so-called bridges, between pairs of DNA molecules may generate a super liquid-crystalline structure (BR-phase). The latter could have a layered spatial structure and an abnormal optical activity that could have a bearing upon the intense CD-band observed in DNA-dispersions.

cond-mat.soft↗