scholarly journals Total decay and transition rates from LQCD

2018 ◽  
Vol 175 ◽  
pp. 13021
Author(s):  
Maxwell T. Hansen ◽  
Harvey B. Meyer ◽  
Daniel Robaina
Keyword(s):  
Spectral Function ◽  
Infinite Volume ◽  
Final States ◽  
Transition Rates ◽  
Lattice Data ◽  
Point Function ◽  
Volume Limit ◽  
A New Technique ◽  
Infinite Volume Limit ◽  
Smoothing Procedure

We present a new technique for extracting total transition rates into final states with any number of hadrons from lattice QCD. The method involves constructing a finite-volume Euclidean four-point function whose corresponding infinite-volume spectral function gives access to the decay and transition rates into all allowed final states. The inverse problem of calculating the spectral function is solved via the Backus-Gilbert method, which automatically includes a smoothing procedure. This smoothing is in fact required so that an infinite-volume limit of the spectral function exists. Using a numerical toy example we find that reasonable precision can be achieved with realistic lattice data. In addition, we discuss possible extensions of our approach and, as an example application, prospects for applying the formalism to study the onset of deep-inelastic scattering. More details are given in the published version of this work, Ref. [1].

scholarly journals Tree Polymers in the Infinite Volume Limit at Critical Strong Disorder

2011 ◽  
Vol 48 (03) ◽  
pp. 885-891
Author(s):  
Torrey Johnson ◽  
Edward C. Waymire
Keyword(s):  
Asymptotic Variance ◽  
Standard Theory ◽  
Convergence In Probability ◽  
Infinite Volume ◽  
Weak Disorder ◽  
Branching Random Walks ◽  
Strong Disorder ◽  
Volume Limit ◽  
Specific Formula ◽  
Infinite Volume Limit

The almost-sure existence of a polymer probability in the infinite volume limit is readily obtained under general conditions of weak disorder from standard theory on multiplicative cascades or branching random walks. However, speculations in the case of strong disorder have been mixed. In this note existence of an infinite volume probability is established at critical strong disorder for which one has convergence in probability. Some calculations in support of a specific formula for the almost-sure asymptotic variance of the polymer path under strong disorder are also provided.

scholarly journals Non-integrable Ising Models in Cylindrical Geometry: Grassmann Representation and Infinite Volume Limit

2021 ◽  
Author(s):  
Giovanni Antinucci ◽  
Alessandro Giuliani ◽  
Rafael L. Greenblatt
Keyword(s):  
Nearest Neighbor ◽  
Scaling Limit ◽  
Ising Models ◽  
Infinite Volume ◽  
Effective Potentials ◽  
Volume Limit ◽  
Cylindrical Domains ◽  
Key Aspects ◽  
Infinite Volume Limit ◽  
Detailed Derivation

AbstractIn this paper, meant as a companion to Antinucci et al. (Energy correlations of non-integrable Ising models: the scaling limit in the cylinder, 2020. arXiv: 1701.05356), we consider a class of non-integrable 2D Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green’s function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.

scholarly journals QUANTUM NOISE INDUCED ENTANGLEMENT AND CHAOS IN THE DISSIPATIVE QUANTUM MODEL OF BRAIN

2004 ◽  
Vol 18 (06) ◽  
pp. 841-858 ◽  
Author(s):  
ELIANO PESSA ◽  
GIUSEPPE VITIELLO
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Noise ◽  
Random Force ◽  
Quantum Model ◽  
Infinite Volume ◽  
Quantum Dissipation ◽  
Memory Space ◽  
Volume Limit ◽  
System Ground State ◽  
Infinite Volume Limit

We discuss some features of the dissipative quantum model of brain in the frame of the formalism of quantum dissipation. Such a formalism is based on the doubling of the system degrees of freedom. We show that the doubled modes account for the quantum noise in the fluctuating random force in the system-environment coupling. Remarkably, such a noise manifests itself through the coherent structure of the system ground state. The entanglement of the system modes with the doubled modes is shown to be permanent in the infinite volume limit. In such a limit the trajectories in the memory space are classical chaotic trajectories.

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