Retrieval Properties of Hopfield and Correlated Attractors in an Associative Memory Model

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including correlated attractors was reported in the cases of finite and infinite loading. In this paper, by means of a statistical mechanical method, we study the statics and dynamics of the model in both finite and extensive loading, mainly focusing on the retrieval properties of the Hopfield and correlated attractors. In the extensive loading case, we derive the evolution equations by the dynamical replica theory. We found several characteristic temporal behaviours, both in the finite and extensive loading cases. The theoretical results were confirmed by numerical simulations.Comment: 12 pages, 7 figure

Magnetic strong coupling in a spin-photon system and transition to classical regime

We study the energy level structure of the Tavis-Cumming model applied to an ensemble of independent magnetic spins $s=1/2$ coupled to a variable number of photons. Rabi splittings are calculated and their distribution is analyzed as a functin of photon number $n_{\rm max}$ and spin system size $N$. A sharp transition in the distribution of the Rabi frequency is found at $n_{\rm max}\approx N$. The width of the Rabi frequency spectrum diverges as $\sqrt{N}$ at this point. For increased number of photons $n_{\rm max}>N$, the Rabi frequencies converge to a value proportional to $\sqrt{n_{\rm max}}$. This behavior is interpreted as analogous to the classical spin resonance mechanism where the photon is treated as a classical field and one resonance peak is expected. We also present experimental data demonstrating cooperative, magnetic strong coupling between a spin system and photons, measured at room temperature. This points towards quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques.Comment: Received 8 April 2010; revised manuscript received 17 June 2010; published 14 July 201

Quantum Monte Carlo Study on Magnetization Processes

A quantum Monte Carlo method combining update of the loop algorithm with the global flip of the world line is proposed as an efficient method to study the magnetization process in an external field, which has been difficult because of inefficiency of the update of the total magnetization. The method is demonstrated in the one dimensional antiferromagnetic Heisenberg model and the trimer model. We attempted various other Monte Carlo algorithms to study systems in the external field and compared their efficiency.Comment: 5 pages, 9 figures; added references for section 1, corrected typo

Nonexponential Relaxation of Magnetization at the Resonant Tunneling Point under a Fluctuating Random Noise

Nonexponential relaxation of magnetization at resonant tunneling points of nanoscale molecular magnets is interpreted to be an effect of fluctuating random field around the applied field. We demonstrate such relaxation in Langevin equation analysis and clarify how the initial relaxation (square-root time) changes to the exponential decay. The scaling properties of the relaxation are also discussed.Comment: 4 pages, 4 fgiure

Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

We study the three-dimensional generalized six-state clock model at values of the energy parameters, at which the system is considered to have the same behavior as the stacked triangular antiferromagnetic Ising model and the three-state antiferromagnetic Potts model. First, we investigate ordered phases by using the Monte Carlo twist method (MCTM). We confirmed the existence of an incompletely ordered phase (IOP1) at intermediate temperature, besides the completely ordered phase (COP) at low-temperature. In this intermediate phase, two neighboring states of the six-state model mix, while one of them is selected in the low temperature phase. We examine the fluctuation the mixing rate of the two states in IOP1 and clarify that the mixing rate is very stable around 1:1. The high temperature phase transition is investigated by using non-equilibrium relaxation method (NERM). We estimate the critical exponents beta=0.34(1) and nu=0.66(4). These values are consistent with the 3D-XY universality class. The low temperature phase transition is found to be of first-order by using MCTM and the finite-size-scaling analysis

The Mu2e crystal calorimeter

The Mu2e Experiment at Fermilab will search for coherent, neutrino-less conversion of negative muons into electrons in the field of an Aluminum nucleus, μ− + Al → e− +Al. Data collection start is planned for the end of 2021. The dynamics of such charged lepton flavour violating (CLFV) process is well modelled by a two-body decay, resulting in a mono-energetic electron with an energy slightly below the muon rest mass. If no events are observed in three years of running, Mu2e will set an upper limit on the ratio between the conversion and the capture rates R_μe = μ− + A(Z,N) → e− + A(Z,N)/μ− + A(Z,N) → ν_μ− + A(Z−1,N) of ≤ 6 × 10^(−17) (@ 90% C.L.). This will improve the current limit of four order of magnitudes with respect to the previous best experiment. Mu2e complements and extends the current search for μ → e γ decay at MEG as well as the direct searches for new physics at the LHC. The observation of such CLFV process could be clear evidence for New Physics beyond the Standard Model. Given its sensitivity, Mu2e will be able to probe New Physics at a scale inaccessible to direct searches at either present or planned high energy colliders. To search for the muon conversion process, a very intense pulsed beam of negative muons (~ 10^(10) μ/sec) is stopped on an Aluminum target inside a very long solenoid where the detector is also located. The Mu2e detector is composed of a straw tube tracker and a CsI crystals electromagnetic calorimeter. An external veto for cosmic rays surrounds the detector solenoid. In 2016, Mu2e has passed the final approval stage from DOE and has started its construction phase. An overview of the physics motivations for Mu2e, the current status of the experiment and the required performances and design details of the calorimeter are presented