arXiv subjects

F. Borgonovi

Publications and source records attributed to F. Borgonovi.

At least 37 records · Page 2Linked to original sources

arXiv2010

Dynamics of random dipoles : chaos {\it vs} ferromagnetism

The microcanonical dynamics of an ensemble of random magnetic dipoles in a needle has been investigated. Analyzing magnetic reversal times, a transition between a chaotic paramagnetic phase and an integrable ferromagnetic phase has been numerically found. In particular, a simple criterium for transition has been formulated. Close to the transition point the statistics of average magnetic reversal times and fluctuations have been studied and critical exponents numerically given.

cond-mat.stat-mech↗

arXiv2010

Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes (BS) expression with volatility in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile.

q-fin.PR↗

arXiv2010

Evolution of Entanglement of Two Qubits Interacting through Local and Collective Environments

We analyze rigorously the dynamics of the entanglement between two qubits which interact only through collective and local environments. Our approach is based on the resonance perturbation theory which assumes a small interaction between the qubits and the environments. The main advantage of our approach is that the expressions for (i) characteristic time-scales, such as decoherence, disentanglement, and relaxation, and (ii) observables are not limited by finite times. We introduce a new classification of decoherence times based on clustering of the reduced density matrix elements. The characteristic dynamical properties such as creation and decay of entanglement are examined. We also discuss possible applications of our results for superconducting quantum computation and quantum measurement technologies.

quant-ph↗

arXiv2007

Magnetic Reversal Time in Open Long Range Systems

Topological phase space disconnection has been recently found to be a general phenomenon in isolated anisotropic spin systems. It sets a general framework to understand the emergence of ferromagnetism in finite magnetic systems starting from microscopic models without phenomenological on-site barriers. Here we study its relevance for finite systems with long range interacting potential in contact with a thermal bath. We show that, even in this case, the induced magnetic reversal time is exponentially large in the number of spins, thus determining {\it stable} (to any experimental observation time) ferromagnetic behavior. Moreover, the explicit temperature dependence of the magnetic reversal time obtained from the microcanonical results, is found to be in good agreement with numerical simulations. Also, a simple and suggestive expression, indicating the Topological Energy Threshold at which the disconnection occurs, as a real energy barrier for many body systems, is obtained analytically for low temperature.

cond-mat.stat-mech↗

arXiv2007

Controllable Adiabatic Manipulation of the Qubit State

We propose a scheme which implements a controllable change of the state of the target spin qubit in such a way that both the control and the target spin qubits remain in their ground states. The interaction between the two spins is mediated by an auxiliary spin, which can transfer to its excited state. Our scheme suggests a possible relationship between the gate and adiabatic quantum computation.

quant-ph↗

arXiv2005

Frequency shift in the oscillating cantilever-driven adiabatic reversals technique as a function of the spin location

The theory of the oscillating cantilever-driven adiabatic reversals (OSCAR) in magnetic resonance force microscopy (MRFM) is extended to describe the relation between an external magnetic field and a dipole magnetic field for an arbitrary location of the single spin. An analytical estimate for the OSCAR MRFM frequency shift is derived and shown to be in excellent agreement with numerical simulations. The dependence of the frequency shift on the position of the spin relative to the cantilever has characteristic maxima and minima which can be used to determine the spin location experimentally.

cond-mat.other↗

arXiv2005

The Topological Non-connectivity Threshold in quantum long-range interacting spin systems

Quantum characteristics of the Topological Non-connectivity Threshold (TNT), introduced in F.Borgonovi, G.L.Celardo, M.Maianti, E.Pedersoli, J. Stat. Phys., 116, 516 (2004), have been analyzed in the hard quantum regime. New interesting perspectives in term of the possibility to study the intriguing quantum-classical transition through Macroscopic Quantum Tunneling have been addressed.

cond-mat.stat-mech↗

arXiv2005

Topological Non--connectivity Threshold in long-range spin systems

We demonstrate the existence of a topological disconnection threshold, recently found in Ref. \cite{JSP}, for generic $1-d$ anisotropic Heisenberg models interacting with an inter--particle potential $R^{-α}$ when $0<α< 1$ (here $R$ is the distance among spins). We also show that if $α$ is greater than the embedding dimension $d$ then the ratio between the disconnected energy region and the total energy region goes to zero when the number of spins becomes very large. On the other hand, numerical simulations in $d=2,3$ for the long-range case $α< d$ support the conclusion that such a ratio remains finite for large $N$ values. The disconnection threshold can thus be thought as a distinctive property of anisotropic long-range interacting systems.

cond-mat.stat-mech↗

arXiv2005

The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal

We prove the existence of a non-ergodicity threshold for an anisotropic classical Heisenberg model with all-to-all couplings. Below the threshold, the energy surface is disconnected in two components with positive and negative magnetizations respectively. Above, in a fully chaotic regime, magnetization changes sign in a stochastic way and its behavior can be fully characterized by an average magnetization reversal time. We show that statistical mechanics predicts a phase--transition at an energy higher than the non-ergodicity threshold. We assess the dynamical relevance of the latter for finite systems through numerical simulations and analytical calculations. In particular, the time scale for magnetic reversal diverges as a power law at the ergodicity threshold with a size-dependent exponent, which could be a signature of the phenomenon.

cond-mat.stat-mech↗

arXiv2005

Quantum Signatures of The Classical Disconnection Border

A quantum Heisenberg model with anisotropic coupling and all-to-all interaction has been analyzed using the Bose-Einstein statistics. In Ref.\cite{jsp} the existence of a classical energy disconnection border (EDB) in the same kind of models has been demonstrated. We address here the problem to find quantum signatures of the EDB. An independent definition of a quantum disconnection border, motivated by considerations strictly valid in the quantum regime is given. We also discuss the dynamical relevance of the quantum border with respect to quantum magnetic reversal. Contrary to the classical case the magnetization can flip even below the EDB through Macroscopic Quantum Tunneling. We evaluate the time scale for magnetic reversal from statistical and spectral properties, for a small number of particles and in the semiclassical limit.

cond-mat.other↗

arXiv2004

Modeling and Simulations of a Single-Spin Measurement using MRFM

We review the quantum theory of a single spin magnetic resonance force microscopy (MRFM). We concentrate on the novel technique called oscillating cantilever-driven adiabatic reversals (OSCAR), which has been used for a single spin detection (Dan Rugar, Talk on the 2004 IEEE NTC Quantum Device Technology Workshop). First we describe the quantum dynamics of the cantilever-spin system using simple estimates in the spirit of the mean field approximation. Then we present the results of our computer simulations of the Schrodinger equation for the wave function of the cantilever-spin system and of the master equation for the density matrix of the system. We demonstrate that the cantilever behaves like a quasi-classical measurement device which detects the spin projection along the effective magnetic field. We show that the OSCAR technique provides continuous monitoring of the single spin, which could be used to detect the mysterious quantum collapses of the wave function of the cantilever-spin system.

quant-ph↗

arXiv2004

Wave function collapses in a single spin magnetic resonance force microscopy

We study the effects of wave function collapses in the oscillating cantilever driven adiabatic reversals (OSCAR) magnetic resonance force microscopy (MRFM) technique. The quantum dynamics of the cantilever tip (CT) and the spin is analyzed and simulated taking into account the magnetic noise on the spin. The deviation of the spin from the direction of the effective magnetic field causes a measurable shift of the frequency of the CT oscillations. We show that the experimental study of this shift can reveal the information about the average time interval between the consecutive collapses of the wave function

quant-ph↗

arXiv2004

Broken Ergodicity in classically chaotic spin systems

A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as ergodicity and chaoticity are strongly different. Indeed, even in presence of chaoticity, the model displays a lack of ergodicity only in presence of all to all interaction and below an energy threshold, that persists in the thermodynamical limit. Energy threshold can be found analytically and results can be generalized for a generic XY model with asymmetric coupling.

cond-mat.stat-mech↗

arXiv2004

A Model for Quantum Jumps in Magnetic Resonance Force Microscopy

We propose a simple model which describes the statistical properties of quantum jumps in a single-spin measurement using the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. Our computer simulations based on this model predict the average time interval between two consecutive quantum jumps and the correlation time to be proportional to the characteristic time of the magnetic noise and inversely proportional to the square of the magnetic noise amplitude.

quant-ph↗

arXiv2004

Survival of quantum effects for observables after decoherence

When a quantum nonlinear system is linearly coupled to an infinite bath of harmonic oscillators, quantum coherence of the system is lost on a decoherence time-scale $τ_D$. Nevertheless, quantum effects for observables may still survive environment-induced decoherence, and be observed for times much larger than the decoherence time-scale. In particular, we show that the Ehrenfest time, which characterizes a departure of quantum dynamics for observables from the corresponding classical dynamics, can be observed for a quasi-classical nonlinear oscillator for times $τ\ggτ_D$. We discuss this observation in relation to recent experiments on quantum nonlinear systems in the quasi-classical region of parameters.

quant-ph↗

arXiv2003

Irregular Dynamics in a One-Dimensional Bose System

We study many-body quantum dynamics of $δ$-interacting bosons confined in a one-dimensional ring. Main attention is payed to the transition from the mean-field to Tonks-Girardeau regime using an approach developed in the theory of interacting particles. We analyze, both analytically and numerically, how the Shannon entropy of the wavefunction and the momentum distribution depend on time for a weak and strong interactions. We show that the transition from regular (quasi-periodic) to irregular ("chaotic") dynamics coincides with the onset of the Tonks-Girardeau regime. In the latter regime the momentum distribution of the system reveals a statistical relaxation to a steady state distribution. The transition can be observed experimentally by studying the interference fringes obtained after releasing the trap and letting the boson system expand ballistically.

cond-mat.stat-mech↗

arXiv2003

Quantum Dynamics of the Oscillating Cantilever-Driven Adiabatic Reversals in Magnetic Resonance Force Microscopy

We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schrodinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.

quant-ph↗

arXiv2002

Single-Spin Measurement and Decoherence in Magnetic Resonance Force Microscopy

We consider a simple version of a cyclic adiabatic inversion (CAI) technique in magnetic resonance force microscopy (MRFM). We study the problem: What component of the spin is measured in the CAI MRFM? We show that the non-destructive detection of the cantilever vibrations provides a measurement of the spin component along the effective magnetic field. This result is based on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation) and the numerical solution of the master equation.

quant-ph↗