arXiv subjects

S. Nicolis

Publications and source records attributed to S. Nicolis.

At least 19 recordsLinked to original sources

arXiv2020

Dynamics of contact epidemic models for finite populations

We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as in terms of a stochastic formulation. At the level of the deterministic equations, we deduce relations between the parameters of the model for the disease to become endemic. Within the stochastic formulation, it is possible to write recursion relations for the probability distribution, that lead to exact expression for some of its moments and check the validity of the stochastic threshold theorems.

q-bio.PE↗

arXiv2014

Information processing with Page-Wootters states

In order to perceive that a physical system evolves in time, two requirements must be met: (a) it must be possible to define a "clock" and (b) it must be possible to make a copy of the state of the system, that can be reliably retrieved to make a comparison. We investigate what constraints quantum mechanics poses on these issues, in light of recent experiments with entangled photons.

quant-ph↗

arXiv2014

A particle in equilibrium with a bath realizes worldline supersymmetry

We study the relation between the partition function of a non--relativistic particle, in one spatial dimension, that describes the equilibrium fluctuations implicitly, and the partition function of the same system, deduced from the Langevin equation, that describes the fluctuations explicitly, of a bath with additive white--noise properties using Monte Carlo simulations for computing the correlation functions that satisfy the corresponding identities. We show that both can be related to the partition function of the corresponding, maximally supersymmetric, theory with one--dimensional bosonic worldvolume, by appropriate analytic continuation, from Euclidian to real time, and that they can all describe the same physics, since the correlation functions of the observables satisfy the same identities for all systems.The supersymmetric theory provides the consistent closure for describing the fluctuations. Therefore supersymmetry is relevant at the scale in which equilibrium with the bath is meaningful. At scales when the "true" degrees of freedom of the bath can be resolved (e.g. atoms and molecules for the case of thermal fluctuations) the superpartners become "hidden". They can be, always, revealed through the identities satisfied by the correlation functions of the appropriate noise field, however. In fact, the same formalism applies whatever the "microscopic" origin of the fluctuations. Therefore, all consistently closed physical systems are supersymmetric--and any system that is explicitly not invariant under supersymmetric transformations, is, in fact, open and, therefore, incomplete.

hep-th↗

arXiv2014

Knotted Strange Attractors and Matrix Lorenz Systems

A generalization of the Lorenz equations is proposed where the variables take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of $\mathfrak{u}(2)$. We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations.

nlin.CD↗

arXiv2014

Modular discretization of the AdS2/CFT1 Holography

We propose a finite discretization for the black hole geometry and dynamics. We realize our proposal, in the case of extremal black holes, for which the radial and temporal near horizon geometry is known to be AdS$_2=SL(2,\mathbb{R})/SO(1,1,\mathbb{R})$. We implement its discretization by replacing the set of real numbers $\mathbb{R}$ with the set of integers modulo $N$, with AdS$_2$ going over to the finite geometry AdS$_2[N]=SL(2,\mathbb{Z}_N)/SO(1,1,\mathbb{Z}_N)$. We model the dynamics of the microscopic degrees of freedom by generalized Arnol'd cat maps, ${\sf A}\in SL(2,\mathbb{Z}_N)$, which are isometries of the geometry at both the classical and quantum levels. These exhibit well studied properties of strong arithmetic chaos, dynamical entropy, nonlocality and factorization in the cutoff discretization $N$, which are crucial for fast quantum information processing. We construct, finally, a new kind of unitary and holographic correspondence, for AdS$_2[N]$/CFT$_1[N]$, via coherent states of both the bulk and boundary geometries.

hep-th↗

arXiv2013

Quantum Mechanics à la Langevin and Supersymmetry

We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under ${\mathcal N}=1$ SUSY, but can be obtained from a, manifestly, supersymmetric expression, upon fixing a local fermionic symmetry, called $κ-$symmetry. The kinetic term for the fermions is a total derivative and can contribute only on the boundaries. We define combinations that scale appropriately, as the lattice spacing is taken to zero and the lattice size to infinity and provide evidence, by numerical simulations, that the correlation functions of the auxiliary field do satisfy Wick's theorem. We show, in particular, that simulations can be carried out using a purely bosonic action. The physical import is that the classical trajectory, $ϕ(τ)$, becomes a (chiral) superfield, $(ϕ(τ),ψ_α(τ),F(τ))$, when quantum fluctuations are taken into account.

hep-lat↗

arXiv2013

Supersymmetric probability distributions

We use anticommuting variables to study probability distributions of random variables, that are solutions of Langevin's equation. We show that the probability density always enjoys "worldpoint supersymmetry". The partition function, however, may not. We find that the domain of integration can acquire a boundary, that implies that the auxiliary field has a non-zero expectation value, signalling spontaneous supersymmetry breaking. This is due to the presence of "fermionic" zeromodes, whose contribution cannot be cancelled by a surface term. This we prove by an explicit calculation of the regularized partition function, as well as by computing the moments of the auxiliary field and checking whether they satisfy the identities implied by Wick's theorem. Nevertheless, supersymmetry manifests itself in the identities that are satisfied by the moments of the scalar, whose expressions we can calculate,for all values of the coupling constant. We also provide some quantitative estimates concerning the visibility of supersymmetry breaking effects in the identities for the moments and remark that the shape of the distribution of the auxiliary field can influence quite strongly how easy it would be to mask them, since the expectation value of the auxiliary field doesn't coincide with its typical value.

hep-th↗

arXiv2009

Nambu Quantum Mechanics on Discrete 3-Tori

We propose a quantization of linear, volume preserving, maps on the discrete and finite 3-torus T_N^3 represented by elements of the group SL(3,Z_N). These flows can be considered as special motions of the Nambu dynamics (linear Nambu flows) in the three dimensional toroidal phase space and are characterized by invariant vectors, a, of T_N^3. We quantize all such flows which are necessarily restricted on a planar two-dimensional phase space, embedded in the 3-torus, transverse to the vector a . The corresponding maps belong to the little group of the vector a in SL(3,Z_N) which is an SL(2,Z_N) subgroup. The associated linear Nambu maps are generated by a pair of linear and quadratic Hamiltonians (Clebsch-Monge potentials of the flow) and the corresponding quantum maps, realize the metaplectic representation of SL(3,Z_N) on the discrete group of three dimensional magnetic translations i.e. the non-commutative 3-torus with deformation parameter the N-th root of unity. Other potential applications of our construction are related to the quantization of deterministic chaos in turbulent maps as well as to quantum tomography of three dimensional objects.

hep-th↗

arXiv2007

Layered Phase Investigations

The extra dimensional defects that are introduced to generate the lattice chiral zero modes are not simply a computational trick, but have interesting physical consequences. After reviewing what is known about the layered phase they can generate, I argue how it is possible to simulate Yang-Mills theories with reduced systematic errors and speculate on how it might be possible to study the fluctuations of the layers' topological charge.

hep-lat↗

arXiv2005

Unitary Evolution on a Discrete Phase Space

We construct unitary evolution operators on a phase space with power of two discretization. These operators realize the metaplectic representation of the modular group SL(2,Z_{2^n}). It acts in a natural way on the coordinates of the non-commutative 2-torus, T_{2^n}^2$ and thus is relevant for non-commutative field theories as well as theories of quantum space-time. The class of operators may also be useful for the efficient realization of new quantum algorithms.

hep-lat↗

arXiv2005

Unitary Evolution on a Phase Space with Power of Two Discretization

We construct quantum evolution operators on the space of states, that realize the metaplectic representation of the modular group SL(2,Z_2^n). This representation acts in a natural way on the coordinates of the non-commutative 2-torus and thus is relevant for noncommutative field theories as well as theories of quantum space-time. The larger class of operators, thus defined, may be useful for the more efficient realization of new quantum algorithms.

hep-th↗

arXiv2002

Non-commutative Solitons in Finite Quantum Mechanics

We construct the unitary evolution operators that realize the quantization of linear maps of SL(2,R) over phase spaces of arbitrary integer discretization N and show the non-trivial dependence on the arithmetic nature of N. We discuss the corresponding uncertainty principle and construct the corresponding coherent states, that may be interpreted as non-commutative solitons.

hep-lat↗

arXiv2001

Multi-Layer Structure in the Strongly Five Dimensional Abelian Higgs Model

We explore the phase diagram of the 5--D anisotropic Abelian Higgs model by Monte Carlo simulations. In particular, we study the transition between the confining phase and the four dimensional layered Higgs phase. We find that, in a certain region of the lattice parameter space, this transition can be first order and that each layer moves into the Higgs phase independently of the others (decoupling of layers).

hep-lat↗

arXiv2001

Branes in the 5D Abelian Higgs Model

We find 3-brane Higgs and Coulomb phases in the 5D Abelian Higgs Model and determine the transition surfaces that separate them from the usual bulk phases.

hep-lat↗

arXiv2001

Multi--Layer Structure in the Strongly Coupled 5D Abelian Higgs Model

We explore the phase diagram of the five-dimensional anisotropic Abelian Higgs model by Monte Carlo simulations. In particular, we study the transition between the confining phase and the four dimensional layered Higgs phase. We find that, in a certain region of the lattice parameter space, this transition can be first order and that each layer moves into the Higgs phase independently of the others (decoupling of layers). As the Higgs couplings vary, we find, using mean field techniques, that this transition may probably become second order.

hep-lat↗

arXiv2000

Phase Structure of the 5D Abelian Higgs Model with Anisotropic Couplings

We establish the phase diagram of the five-dimensional anisotropic Abelian Higgs model by mean field techniques and Monte Carlo simulations. The anisotropy is encoded in the gauge couplings as well as in the Higgs couplings. In addition to the usual bulk phases (confining, Coulomb and Higgs) we find four-dimensional ``layered'' phases (3-branes) at weak gauge coupling, where the layers may be in either the Coulomb or the Higgs phase, while the transverse directions are confining.

hep-lat↗

arXiv2000

Quantum Mechanics on the Hypercube

We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this representation acts in a natural way on the coordinates of the non-commutative 2-torus,T^2, and thus is relevant for noncommutative field theories as well as theories of quantum space-time.

hep-th↗

arXiv1998

Fast Quantum Maps

We develop number theoretic tools that allow to perform computations relevant for the quantum mechanics over finite fields of arbitrary, odd size, with the same speedup that is enjoyed by the Fast Fourier Transform.

math-ph↗