# Vitaly VanchurinUniversity of Minnesota Duluth | UMD · Department of Physics

Vitaly Vanchurin

PhD

## About

60

Publications

10,620

Reads

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1,353

Citations

Introduction

quantum cosmology, quantum gravity, quantum information, machine learning

Additional affiliations

July 2017 - present

August 2012 - June 2017

August 2009 - August 2012

## Publications

Publications (60)

We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph that contains necessary and sufficient information for computing the full quantum partition function. We derive a second-order differen...

We analyze algorithmic and computational aspects of biological phenomena, such as replication and programmed death, in the context of machine learning. We use two different measures of neuron efficiency to develop machine learning algorithms for adding neurons to the system (i.e. replication algorithm) and removing neurons from the system (i.e. pro...

We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for minimization of the loss function is employed to derive a canonical ensemble of organisms (population), the correspon...

We apply the theory of learning to physically renormalizable systems in an attempt to outline a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution that appear to be necessary and sufficient to render a universe observable and show that they entail the major fe...

Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g., state of neurons) and slow-changing trainable variables (e.g., weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of ne...

We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for minimization of the loss function is employed to derive a canonical ensemble of organisms (population), the correspon...

Neural network is a dynamical system described by two different types of degrees of freedom: fast-changing non-trainable variables (e.g. state of neurons) and slow-changing trainable variables (e.g. weights and biases). We show that the non-equilibrium dynamics of trainable variables can be described by the Madelung equations, if the number of neur...

We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution that appear to be necessary and sufficient to render a universe observable and show that they entail the major fe...

It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schrödinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden variables. We consider instead a grand canonical ensemble of neural networks, by allowing an exchange of neuron...

We demonstrate, both analytically and numerically, that learning dynamics of neural networks is generically attracted towards a self-organized critical state. The effect can be modeled with quartic interactions between non-trainable variables (e.g. states of neurons) and trainable variables (e.g. weight matrix). Non-trainable variables are rapidly...

We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived starting from non-interacting subsystems at zeroth order and then by introducing couplings of increasing complex...

It was recently shown that the Madelung equations, that is, a hydrodynamic form of the Schr\"odinger equation, can be derived from a canonical ensemble of neural networks where the quantum phase was identified with the free energy of hidden variables. We consider instead a grand canonical ensemble of neural networks, by allowing an exchange of neur...

We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom: “trainable” variables (e.g., bias vector or weight matrix) and “hidden” variables (e.g., state vector of neurons). We first consider stochastic evolution of the trainable variables to...

We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom: "trainable" variables (e.g. bias vector or weight matrix) and "hidden" variables (e.g. state vector of neurons). We first consider stochastic evolution of the trainable variables to ar...

We define a neural network as a septuple consisting of (1) a state vector, (2) an input projection, (3) an output projection, (4) a weight matrix, (5) a bias vector, (6) an activation map and (7) a loss function. We argue that the loss function can be imposed either on the boundary (i.e. input and/or output neurons) or in the bulk (i.e. hidden neur...

We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of the Markov chain is given and the conserved quantities are known to exist, but not explicitly given. To study t...

We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived starting from non-interacting subsystems at zeroth order and then by introducing couplings of increasing complex...

We consider finite quantum systems defined by a mixed set of commutation and anti-commutation relations between components of the Hamiltonian operator. These relations are represented by an anti-commutativity graph which contains a necessary and sufficient information for computing the full quantum partition function. We derive a second-order diffe...

We consider the quantum partition function for a system of quantum spinors and then derive an equivalent (or dual) classical partition function for some scalar degrees of freedom. The coupling between scalars is non-trivial (e.g. a model on 2-sphere configuration space), but the locality structure of the dual system is preserved, in contrast to the...

We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of quantities on long time-scales. We assume that the transition matrix of the Markov chain is given and the conserved quantities are known to exist, but not explicitly given. To study the stoc...

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of...

Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as macroscopic constraints we consider statistical ensembles over the space of classical probability distributions or...

We find two families of analytic solutions to the ideal magnetohydrodynamics (iMHD) equations, in a class of 4-dimensional (4D) curved spacetimes. The plasma current is null, and as a result, the stress-energy tensor of the plasma itself can be chosen to take a cosmological-constant-like form. Despite the presence of a plasma, the force-free condit...

Given two quantum states of $N$ q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large $N$ limit the quantum maze problem is equivalent to the problem of...

We describe a simple computational model of cosmic logic suitable for
analysis of, for example, discretized cosmological systems. The construction is
based on a particular model of computation, developed by Alan Turing, with
cosmic observers (CO), cosmic measures (CM) and cosmic symmetries (CS)
described by Turing machines. CO machines always start...

We consider generating functionals for computing correlators in quantum field
theories with random potentials. Examples of such theories include condensed
matter systems with quenched disorder (e.g. spin glass) or cosmological systems
in context of the string theory landscape (e.g. cosmic inflation). We use the
so-called replica trick to define two...

We develop a field theory description of non-dissipative string fluids and
construct an explicit mapping between field theory degrees of freedom and
hydrodynamic variables. The theory generalizes both a perfect particle fluid
and pressureless string fluid to what we call a perfect string fluid. Ideal
magnetohydrodynamics is shown to be an example o...

We discuss eternal inflation in context of classical probability spaces
defined by a triplet: sample space, $\sigma$-algebra and probability measure.
We show that the measure problem is caused by the countable additivity axiom
applied to the maximal $\sigma$-algebra of countably infinite sample spaces.
This is a serious problem if the bulk space-ti...

We study the solutions of string fluid equations under assumption of a local
equilibrium which was previously obtained in the context of the kinetic theory.
We show that the fluid can be foliated into non-interacting submanifolds whose
equations of motion are exactly that of the wiggly strings considered
previously by Vilenkin and Carter. In a spec...

We consider a covariant approach to coarse-graining a network of interacting
Nambu-Goto strings. A transport equation is constructed for a spatially flat
Friedmann universe. In Minkowski space and with no spatial dependence this
model agrees with a previous model. Thus it likewise converges to an
equilibrium with a factorizability property. We pres...

We consider conserved currents in an interacting network of one-dimensional
objects (or strings). Singular currents localized on a single string are
considered in general, and a formal procedure for coarse-graining over many
strings is developed. This procedure is applied to strings described by the
Nambu-Goto action such as cosmic strings. In addi...

DOI:https://doi.org/10.1103/PhysRevD.87.069910

We develop further a kinetic theory of strings and derive a transport
equation for a network of cosmic strings with Nambu-Goto evolution,
interactions and background gravitational effects taken into account. We prove
an H-theorem and obtain necessary and sufficient conditions for a thermodynamic
equilibrium. At the lowest order the equilibrium is e...

There are two main approaches to non-equlibrium statistical mechanics: one
using stochastic processes and the other using dynamical systems. To model the
dynamics during inflation one usually adopts a stochastic description, which is
known to suffer from serious conceptual problems. To overcome the problems
and/or to gain more insight, we develop a...

The definition of probabilities in eternally inflating universes requires a
measure to regulate the infinite spacetime volume, and much of the current
literature uses a global time cutoff for this purpose. Such measures have been
found to lead to paradoxical behavior, and recently Bousso, Freivogel,
Leichenauer, and Rosenhaus have argued that, unde...

We study the dynamics of strings by means of a distribution function f(A, B,
x, t) defined on a 9+1D phase space, where A and B are the correlation vectors
of right- and left-moving waves. We derive a transport equation (an analogous
to Boltzmann transport equation for particles) that governs the evolution of
long strings with Nambu-Goto dynamics a...

Many probability measures in the multiverse depend exponentially on some observable parameters, giving rise to potential problems such as youngness bias, Q-catastrophe etc. In this paper we explore a possibility that the exponential runaway dependence should be viewed not as a problem, but as a feature that may help us to fix all parameters in the...

At early stages the dynamics of cosmic string networks is expected to be influenced by an excessive production of small loops at the scales of initial conditions lmin. To understand the late time behavior we propose a very simple analytical model of strings with a nonscaling population of loops. The complicated nonlinear dynamics is described by o...

We show that most of cutoff measures of the multiverse violate some of the
basic properties of probability theory when applied repeatedly to predict the
results of local experiments. Starting from minimal assumptions, such as Markov
property, we derive a correspondence between cosmological measures and quantum
field theories in one lesser dimension...

We develop a model of string dynamics with back-reaction
from both scaling and non-scaling loops taken into account. The
evolution of a string network is described by the distribution
functions of coherence segments and kinks. We derive two non-linear
equations which govern the evolution of the two distributions and
solve them analytically in the l...

We argue that the total number of distinguishable locally Friedmann universes generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the number of e-folds of slow-roll post-eternal inflation. For simplest models of chaotic inflation, N is approximately eq...

We analyze statistical properties of the separate multipole moments of the CMB temperature maps and find that the distribution tails are slightly non-Gaussian. Moreover, the deviation from Gaussianity peaks sharply at around $l\sim45\pm10$. If the detected non-Gaussianities should be attributed to the remaining foreground contamination from the gal...

We analyze the behavior of linear perturbations in vector inflation. In contrast to the scalar field inflation, the linearized theory with vector fields contains couplings between scalar, vector and tensor modes. The perturbations decouple only in the ultraviolet limit, which allows us to carry out the canonical quantization. Superhorizon perturbat...

We study the recently proposed ''stationary measure'' in the
context of the string landscape scenario. We show that it suffers neither from the ''Boltzmann brain'' problem nor from the
''youngness'' paradox that makes some other measures predict a high
CMB temperature at present. We also demonstrate a good performance
of this measure in predicting...

We discuss the gravitational waves (GW) in the context of vector inflation. We derive the
action for tensor perturbations and find that tachyonic instabilities are present in most
(but not all) of the inflationary models with large fields. In contrast, the stability of the
small field inflation () is ensured by the usual slow-roll conditions, where...

We propose a scenario where inflation is driven by non-minimally coupled massive vector fields. In an isotropic homogeneous universe these fields behave in presicely the same way as a massive minimally coupled scalar field. Therefore our model is very similar to the model of chaotic inflation with scalar field. For vector fields the isotropy of exp...

We develop an analytical model to study the production spectrum of loops in the cosmic string network. In the scaling regime, we find two different scales corresponding to large (one order below horizon) and small (few orders below horizon) loops. The very small (tiny) loops at the gravitational back reaction scale are absent, and thus, our model h...

Cosmological scenarios with k-essence are invoked in order to explain the observed late-time acceleration of the universe. These scenarios avoid the need for fine-tuned initial conditions (the "coincidence problem") because of the attractor-like dynamics of the k-essence field \phi. It was recently shown that all k-essence scenarios with Lagrangian...

We propose a numerical test of fundamental physics based on the complexity measure of a general set of functions, which is directly related to the Kolmogorov (or algorithmic) complexity studied in mathematics and computer science. The analysis can be carried out for any scientific experiment and might lead to a better understanding of the underlyin...

We study the landscape models of eternal inflation with an arbitrary number of different vacua states, both recyclable and terminal. We calculate the abundances of bubbles following different geodesics. We show that the results obtained from generic time-like geodesics have undesirable dependence on initial conditions. In contrast, the predictions...

We study the production of loops in the cosmic string network in the expanding background by means of a numerical simulation exact in the flat-spacetime limit and first-order in the expansion rate. We find an initial regime characterized by production of small loops at the scale of the initial correlation length, but later we see the emergence of a...

We study a class of ``landscape'' models in which all vacua have positive energy density, so that inflation never ends and bubbles of different vacua are endlessly ``recycled''. In such models, each geodesic observer passes through an infinite sequence of bubbles, visiting all possible kinds of vacua. The bubble abundance $p_j$ can then be defined...

We study the spectrum of loops as a part of a complete network of cosmic strings in flat spacetime. After a long transient regime, characterized by production of small loops at the scale of the initial conditions, it appears that a true scaling regime takes over. In this final regime the characteristic length of loops scales as $0.1 t$, in contrast...

We investigate the evolution of cosmic strings network in flat space. We
give a dynamical argument that the structures on infinite strings should
obey a scaling law. We perform a simulation of the network which uses
functional forms for the string position and thus is exact to the limits
of computer arithmetic. Our results confirm that the wiggles...

We investigate the evolution of infinite strings as a part of a complete
cosmic string network in flat space. We perform a simulation of the network
which uses functional forms for the string position and thus is exact to the
limits of computer arithmetic. Our results confirm that the wiggles on the
strings obey a scaling law described by universal...

Models of inflationary cosmology can lead to variation of observable parameters ("constants of Nature") on extremely large scales. The question of making probabilistic predictions for today's observables in such models has been investigated in the literature. Because of the infinite thermalized volume resulting from eternal inflation, it has proven...

## Projects

Projects (2)

To study different physical, biological and social phenomena using the theory of neural networks.

The aim of this project is to derive an approximate behavior of quantum systems by adopting the tools of statistical mechanics. Just like thermodynamics can be derived from classical mechanics with many degrees of freedom we expect gravity can be derived from quantum mechanics with many degrees of freedom.