Ensemble interpretation ofL(S)DA+U

2009 ◽  
Vol 80 (24) ◽  
Author(s):  
Igor Chaplygin
Keyword(s):  
Ensemble Interpretation

Synaptic and Temporal Ensemble Interpretation of Spike-Timing-Dependent Plasticity

2005 ◽  
Vol 17 (11) ◽  
pp. 2316-2336 ◽  
Author(s):  
Peter A. Appleby ◽  
Terry Elliott
Keyword(s):  
Neuronal Plasticity ◽  
Spike Timing ◽  
Experimental Results ◽  
Coincidence Detection ◽  
Spatial Averaging ◽  
Critical Window ◽  
Dependent Plasticity ◽  
Minimal Form ◽  
Temporal And Spatial ◽  
Ensemble Interpretation

We postulate that a simple, three-state synaptic switch governs changes in synaptic strength at individual synapses. Under this switch rule, we show that a variety of experimental results on timing-dependent plasticity can emerge from temporal and spatial averaging over multiple synapses and multiple spike pairings. In particular, we show that a critical window for the interaction of pre- and postsynaptic spikes emerges as an ensemble property of the collective system, with individual synapses exhibiting only a minimal form of spike coincidence detection. In addition, we show that a Bienenstock-Cooper-Munro—like, rate-based plasticity rule emerges directly from such a model. This demonstrates that two apparently separate forms of neuronal plasticity can emerge from a much simpler rule governing the plasticity of individual synapses.

scholarly journals COSMOLOGICAL PARTICLE CREATION: FLUCTUATIONS AND AN ENSEMBLE PICTURE

2008 ◽  
Vol 17 (13n14) ◽  
pp. 2441-2445 ◽  
Author(s):  
ALI KAYA
Keyword(s):  
Wave Packets ◽  
Particle Creation ◽  
Mean Value ◽  
Time Dependent ◽  
Quantum Fields ◽  
Number Operator ◽  
Expectation Value ◽  
Reheating Process ◽  
Ensemble Interpretation

We point out that in the context of quantum fields in time-dependent classical backgrounds, the number of created particles with a given momentum largely deviates about its mean value. Since the corresponding Fourier modes are nonlocal, this deviation shows that the expectation value of the number operator can make sense only in an ensemble of space–times. Using a complete orthonormal family of localized wave packets, we show how an ensemble interpretation can be given to cosmological particle creation in local terms. The reheating process following inflation is re-examined in the light of this construction.

scholarly journals CORRELATIONS IN ENTANGLED STATES

2006 ◽  
Vol 20 (11n13) ◽  
pp. 1496-1503
Author(s):  
B. C. SANCTUARY
Keyword(s):  
Quantum Mechanics ◽  
Singlet State ◽  
Entangled States ◽  
Quantum Mechanical ◽  
Interpretation Of Quantum Mechanics ◽  
Hidden Variable ◽  
Phase Decoherence ◽  
Classical Correlations ◽  
Spin Pairs ◽  
Ensemble Interpretation

Entangled EPR spin pairs can be treated using the statistical ensemble interpretation of quantum mechanics. As such the singlet state results from an ensemble of spin pairs each with its own specific axis of quantization. This axis acts like a quantum mechanical hidden variable. If the spins lose coherence they disentangle into a mixed state that contains classical correlations. In this paper an infinitesimal phase decoherence is introduced to the singlet state in order to reveal more clearly some of the correlations. It is shown that a singlet state has no classical correlations.

scholarly journals Discreteness and integrality in Conformal Field Theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Justin Kaidi ◽  
Eric Perlmutter
Keyword(s):  
Black Hole Physics ◽  
Fine Tuning ◽  
Two Dimensional ◽  
Modular Functions ◽  
Integral Vector ◽  
Conformal Field ◽  
Conformal Bootstrap ◽  
Conformal Manifolds ◽  
Vector Valued ◽  
Ensemble Interpretation

Abstract Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the space of CFTs is lacking. We systematically study these constraints in two-dimensional, non-holomorphic CFTs, making use of two main mathematical results. First, we prove a theorem constraining the behavior near the cusp of integral, vector-valued modular functions. Second, we explicitly construct non-factorizable, non-holomorphic cuspidal functions satisfying discreteness and integrality, and prove the non-existence of such functions once positivity is added. Application of these results yields several bootstrap-type bounds on OPE data of both rational and irrational CFTs, including some powerful bounds for theories with conformal manifolds, as well as insights into questions of spectral determinacy. We prove that in rational CFT, the spectrum of operator twists $$ t\ge \frac{c}{12} $$ t ≥ c 12 is uniquely determined by its complement. Likewise, we argue that in generic CFTs, the spectrum of operator dimensions $$ \Delta >\frac{c-1}{12} $$ Δ > c − 1 12 is uniquely determined by its complement, absent fine-tuning in a sense we articulate. Finally, we discuss implications for black hole physics and the (non-)uniqueness of a possible ensemble interpretation of AdS3 gravity.

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