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M. V. Altaisky

Publications and source records attributed to M. V. Altaisky.

At least 19 recordsLinked to original sources
arXiv2026

Quantum reservoir networks based on decoherence-free subspaces

We present numerical simulation of a six-qubit quantum reservoir network with an output implemented on a 5-dimensional decoherence-free subspace (DFS), working as a classifier between entangled and product states of the input quantum system, fed to the reservoir during a finite learning time. Since the dynamics of DFS is not affected by external fluctuations, no cooling is required, and the proposed model seems a promising candidate for future quantum artificial intelligence systems working at room temperatures and free of huge energy consumption.

quant-ph↗
arXiv2024

Poincare group spin networks

Spin network technique is usually generalized to relativistic case by changing $SO(4)$ group -- Euclidean counterpart of the Lorentz group -- to its universal spin covering $SU(2)\times SU(2)$, or by using the representations of $SO(3,1)$ Lorentz group. We extend this approach by using inhomogeneous Lorentz group $\mathcal{P}=SO(3,1)\rtimes \mathbb{R}^4$, which results in the simplification of the spin network technique. The labels on the network graph corresponding to the subgroup of translations $\mathbb{R}^4$ make the intertwiners into the products of $SU(2)$ parts and the energy-momentum conservation delta functions. This maps relativistic spin networks to usual Feynman diagrams for the matter fields.

gr-qc↗
arXiv2020

Wavelet regularization of gauge theories

Extending the principle of local gauge invariance $ψ(x)\to \exp\left(\imath \sum_A ω^A(x)T^A \right) ψ(x), x \in \mathbb{R}^d$, with $T^A$ being the generators of the gauge group $\mathcal{A}$, to the fields $ψ(g)\equiv \langle χ|Ω^*(g)|ψ\rangle$, defined on a locally compact Lie group $G$, $g\in G$, where $Ω(g)$ is suitable square-integrable representation of $G$, it is shown that taking the coordinates ($g$) on the affine group, we get a gauge theory that is finite by construction. The renormalization group in the constructed theory relates to each other the charges measured at different scales. The case of the $\mathcal{A}=SU(N)$ gauge group is considered.

hep-th↗
arXiv2018

Renormalization of viscosity in wavelet-based model of turbulence

Statistical theory of turbulence in viscid incompressible fluid, described by the Navier-Stokes equation driven by random force, is reformulated in terms of scale-dependent fields $\mathbf{u}_a(x)$, defined as wavelet-coefficients of the velocity field $\mathbf{u}$ taken at point $x$ with the resolution $a$. Applying quantum field theory approach of stochastic hydrodynamics to the generating functional of random fields $\mathbf{u}_a(x)$, we have shown the velocity field correlators $\langle \mathbf{u}_{a_1}(x_1)\ldots \mathbf{u}_{a_n}(x_n)\rangle$ to be finite by construction for the random stirring force acting at prescribed large scale $L$. The study is performed in $d=3$ dimension. Since there are no divergences, regularization is not required, and the renormalization group invariance becomes merely a symmetry that relates velocity fluctuations of different scales in terms of the Kolmogorov-Richardson picture of turbulence development. The integration over the scale arguments is performed from the external scale $L$ down to the observation scale $A$, which lies in Kolmogorov range $l \ll A \ll L$. Our oversimplified model is full dissipative: interaction between scales is provided only locally by the gradient vertex $(\mathbf{u}\nabla) \mathbf{u}$, neglecting any effects or parity violation that might be responsible for energy backscatter. The corrections to viscosity and the pair velocity correlator are calculated in one-loop approximation. This gives the dependence of turbulent viscosity on observation scale and describes the scale dependence of the velocity field correlations.

physics.flu-dyn↗
arXiv2018

Symmetry and decoherence-free subspaces in quantum neural networks

Evolution of quantum states of array of quantum dots is analyzed by means of numerical solution of the von Neumann equation. For two qubit system with dipole-dipole interaction and common phonon bath the evolution of the symmetric state $\frac{\uparrow\downarrow+\downarrow\uparrow}{\sqrt{2}}$ leads to the mixture of the triplet states, leaving the singlet decoupled. For three qubit system ($D_{1/2}^{\otimes3}=D_{3/2}+2D_{1/2}$) with common phonon bath we observed similar effects within the quartet state $D_{3/2}$ if all qubits were symmetrically connected.

quant-ph↗
arXiv2017

Wavelets and renormalization group in quantum field theory problems

Using continuous wavelet transform it is possible to construct a regularization procedure for scale-dependent quantum field theory models, which is complementary to functional renormalization group method in the sense that it sums up the fluctuations of larger scales in order to get the effective action at small observation scale (M.V.Altaisky, Phys. Rev. D93(2016) 105043. The standard RG results for $ϕ^4$ model are reproduced. The fixed points of the scale-dependent theory are studied in one loop approximation.

hep-th↗
arXiv2016

Consciousness and quantum mechanics of macroscopic systems

We propose the quantum mechanical description of complex systems should be performed using two types of causality relation: the ordering relation ($x\prec y$) and the subset relation ($A\subseteq B$). The structures with two ordering operations, called the causal sites, have been already proposed in context of quantum gravity (Christensen and Crane, 2005). We suggest they are also common to biological physics and may describe how the brain works. In the spirit of the Penrose ideas we identify the geometry of the space-time with universal field of consciousness. The latter has its evident counterparts in ancient Indian philosophy and provides a framework for unification of physical and mental phenomena.

quant-ph↗
arXiv2016

Unifying renormalization group and the continuous wavelet transform

It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier described in {\em Phys.Rev.D} 81(2010)125003, 88(2013)025015, is finite by construction. The space of scale-dependent functions $\{ ϕ_a(x) \}$ is more relevant to physical reality than the space of square-integrable functions $\mathrm{L}^2(R^d)$, because, due to the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than point. The effective action $Γ_{(A)}$ of our theory turns to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet -- an "aperture function" of a measuring device used to produce the snapshot of a field $ϕ$ at the point $x$ with the resolution $a$. The standard RG results for $ϕ^4$ model are reproduced.

physics.gen-ph↗
arXiv2016

On quantization in light-cone variables compatible with wavelet transform

Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts $u(x) = u^+(x) + u^-(x),$ performed with the help of Fourier transform in Minkowski space. That is the commutation relations are being established between non localized solutions of field equations. At the same time the construction of divergence free physical theory requires the separation of the contributions of different space-time scales. In present paper, using the light-cone variables, we propose a quantization procedure which is compatible with separation of scales using continuous wavelet transform, as described in our previous paper Phys.Rev D 88(2013)025015

hep-th↗
arXiv2014

On discrete symmetries and relic radiation anisotropy

It is argued that large scale angle correlations of the Cosmic Microwave Background Radiation (CMBR) temperature fluctuations measured by Wilkinson Microwave Anisotropy Probe (WMAP) mission may have a trace of discrete symmetries of quantum gravity

astro-ph.CO↗
arXiv2013

Quantum field theory without divergences

It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to {\em unmeasurable} (and hence unphysical) quantities. This is because no physical quantity can be measured in a point, but in a region, the size of which is constrained by the resolution of measuring equipment. The incorporation of the resolution into the definition of quantum fields $ϕ(x)\toϕ^{(A)}(x)$ and appropriate change of Feynman rules results in finite values of the Green functions. The Euclidean $ϕ^4$-field theory is taken as an example.

hep-th↗
arXiv2010

A remark on gauge invariance in wavelet-based quantum field theory

Wavelet transform has been attracting attention as a tool for regularization of gauge theories since the first paper of (Federbush, Progr. Theor. Phys. 94, 1135, 1995), where the integral representation of the fields by means of the wavelet transform was suggested: $$A_μ(x) = \frac{1}{C_ψ} \int_{\R_+ \times\R^d} \frac{1}{a^d} g \left(\frac{x-b}{a} \right) A_{μa}(b) \frac{dad^db}{a},$$ with $A_{μa}(b)$ being understood as the fields $A_μ$ measured at point $b\in \R^d$ with resolution $a\in\R_+$. In present paper we consider a wavelet-based theory of gauge fields, provide a counterpart of the gauge transform for the scale-dependent fields: $A_{μa}(x)\to A_{μa}(x)+\d_μf_a(x)$, and derive the Ward-Takahashi identities for them.

hep-th↗
arXiv2009

Quantum kinetic equation before and after Big Bang

The energy dissipation in a gas of structured objects, e.g. molecules, is considered in density matrix formalism. It is shown that the macroscopic irreversibility of the kinetic processes can be considered as a consequence of the microscopic operator ordering. Our approach is free of any special assumptions on the space-time geometry, except for the general causality assumptions, so it can be applied to a wide variety of processes, from the cosmological processes at Big Bang stage till the energy dissipation in molecular gases.

quant-ph↗
arXiv2004

Multiscale theory of turbulence in wavelet representation

We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of its wavelet components, we achieve the cancellation of loop divergences in the stochastic perturbation expansion. An extra contribution to the energy transfer from large to smaller scales is considered. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures based on the wavelet decomposition are constructed.

cond-mat.soft↗
arXiv2004

Langevin equation with scale-dependent noise

A new wavelet based technique for the perturbative solution of the Langevin equation is proposed. It is shown that for the random force acting in a limited band of scales the proposed method directly leads to a finite result with no renormalization required. The one-loop contribution to the Kardar-Parisi-Zhang equation Green function for the interface growth is calculated as an example.

cond-mat↗