Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

Discontinuous percolation transitions in real physical systems

We study discontinuous percolation transitions (PT) in the diffusion-limited cluster aggregation model of the sol-gel transition as an example of real physical systems, in which the number of aggregation events is regarded as the number of bonds occupied in the system. When particles are Brownian, in which cluster velocity depends on cluster size as $v_s \sim s^{\eta}$ with $\eta=-0.5$, a larger cluster has less probability to collide with other clusters because of its smaller mobility. Thus, the cluster is effectively more suppressed in growth of its size. Then the giant cluster size increases drastically by merging those suppressed clusters near the percolation threshold, exhibiting a discontinuous PT. We also study the tricritical behavior by controlling the parameter $\eta$, and the tricritical point is determined by introducing an asymmetric Smoluchowski equation.Comment: 5 pages, 5 figure

Negative Interactions in Irreversible Self-Assembly

This paper explores the use of negative (i.e., repulsive) interaction the abstract Tile Assembly Model defined by Winfree. Winfree postulated negative interactions to be physically plausible in his Ph.D. thesis, and Reif, Sahu, and Yin explored their power in the context of reversible attachment operations. We explore the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Omega(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate a Turing machine with space bound s and time bound t, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s * t) as required by the standard Turing machine simulation with tiles

BLITZEN: A highly integrated massively parallel machine

The architecture and VLSI design of a new massively parallel processing array chip are described. The BLITZEN processing element array chip, which contains 1.1 million transistors, serves as the basis for a highly integrated, miniaturized, high-performance, massively parallel machine that is currently under development. Each processing element has 1K bits of static RAM and performs bit-serial processing with functional elements for arithmetic, logic, and shifting

On black hole thermalization, D0 brane dynamics, and emergent spacetime

When matter falls past the horizon of a large black hole, the expectation from string theory is that the configuration thermalizes and the information in the probe is rather quickly scrambled away. The traditional view of a classical unique spacetime near a black hole horizon conflicts with this picture. The question then arises as to what spacetime does the probe actually see as it crosses a horizon, and how does the background geometry imprint its signature onto the thermal properties of the probe. In this work, we explore these questions through an extensive series of numerical simulations of D0 branes. We determine that the D0 branes quickly settle into an incompressible symmetric state -- thermalized within a few oscillations through a process driven entirely by internal non-linear dynamics. Surprisingly, thermal background fluctuations play no role in this mechanism. Signatures of the background fields in this thermal state arise either through fluxes, i.e. black hole hair; or if the probe expands to the size of the horizon -- which we see evidence of. We determine simple scaling relations for the D0 branes' equilibrium size, time to thermalize, lifetime, and temperature in terms of their number, initial energy, and the background fields. Our results are consistent with the conjecture that black holes are the fastest scramblers as seen by Matrix theory.Comment: 43 pages, 12 figures; v2: added analysis showing that results are consistent with and confirm Susskind conjecture on black hole thermalization. Added clarification about strong coupling regime. Citation adde

Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature

Frieden and Soffer conjectured some years ago the existence of a ``Fisher temperature" T_F that would play, with regards to Fisher's information measure I, the same role that the ordinary temperature T plays vis-a-vis Shannon's logarithmic measure. Here we exhibit the existence of reciprocity relations between T_F and T and provide an interpretation with reference to the meaning of T_F for the canonical ensemble.Comment: 3 pages, no figure

Sub-milliKelvin spatial thermometry of a single Doppler cooled ion in a Paul trap

We report on observations of thermal motion of a single, Doppler-cooled ion along the axis of a linear radio-frequency quadrupole trap. We show that for a harmonic potential the thermal occupation of energy levels leads to Gaussian distribution of the ion's axial position. The dependence of the spatial thermal spread on the trap potential is used for precise calibration of our imaging system's point spread function and sub-milliKelvin thermometry. We employ this technique to investigate the laser detuning dependence of the Doppler temperature.Comment: 5 pages, 4 figure