In our previous arXiv papers (The Information and the Matter, v1, v5; more systematically the informational conception is presented in the paper The Information as Absolute, 2010) it was rigorously shown that Matter in our Universe - and Universe as
a whole - are some informational systems (structures), which exist as uninterruptedly transforming [practically] infinitesimal sub-sets of the absolutely infinite and fundamental set Information. Such a conception allows not only to clear essentially a number of metaphysical and epistemological problems in philosophy but, besides, allows to suggest a reasonable physical model. Since Matter in Universe is an informational system where any interaction between Matters sub-structures, i.e. - particles and systems of the particles - happens always as an exchange by exclusively true information between these structures, the model is based on the conjecture that Matter is some analogue of computer. The conjecture, in turn, allows to introduce in the model the basic logical elements that constitute the material structures and support the informational exchange - i.e. the forces - between the structures. The model is experimentally testable and yet now makes be more clear a number of basic problems in special relativity, quantum mechanics, and, rather probably, in [now - in Newtonian] gravity.
We construct double cross biproduct and bi-cycle bicrossproduct Lie bialgebras from braided Lie bialgebras. The main result generalizes Majids matched pairs of Lie algebras, Drinfelds quantum double, and Masuokas cross product Lie bialgebras.
We study the time evolution of a system of fermions with pairing interactions at a finite temperature. The dynamics is triggered by an abrupt increase of the BCS coupling constant. We show that if initially the fermions are in a normal phase, the amp
litude of the BCS order parameter averaged over the Boltzman distribution of initial states exhibits damped oscillations with a relatively short decay time. The latter is determined by the temperature, the single-particle level spacing, and the ground state value of the BCS gap for the new coupling. In contrast, the decay is essentially absent when the system was in a superfluid phase before the coupling increase.
We give a two step method to study certain questions regarding associated graded module of a Cohen-Macaulay (CM) module $M$ w.r.t an $mathfrak{m}$-primary ideal $mathfrak{a}$ in a complete Noetherian local ring $(A,mathfrak{m})$. The first step, we c
all it complete intersection approximation, enables us to reduce to the case when both $A$, $ G_mathfrak{a}(A) = bigoplus_{n geq 0} mathfrak{a}^n/mathfrak{a}^{n+1} $ are complete intersections and $M$ is a maximal CM $A$-module. The second step consists of analyzing the classical filtration ${Hom_A(M,mathfrak{a}^n) }_{mathbb{Z}}$ of the dual $Hom_A(M,A)$. We give many applications of this point of view. For instance let $(A,mathfrak{m})$ be equicharacteristic and CM. Let $a(G_mathfrak{a}(A))$ be the $a$-invariant of $G_mathfrak{a}(A)$. We prove: 1. $a(G_mathfrak{a}(A)) = -dim A$ iff $mathfrak{a}$ is generated by a regular sequence. 2. If $mathfrak{a}$ is integrally closed and $a(G_mathfrak{a}(A)) = -dim A + 1$ then $mathfrak{a}$ has minimal multiplicity. We extend to modules a result of Ooishi relating symmetry of $h$-vectors. As another application we prove a conjecture of Itoh, if $A$ is a CM local ring and $mathfrak{a}$ is a normal ideal with $e_3^mathfrak{a}(A) = 0$ then $G_mathfrak{a}(A)$ is CM.
Given a random word of size $n$ whose letters are drawn independently from an ordered alphabet of size $m$, the fluctuations of the shape of the random RSK Young tableaux are investigated, when $n$ and $m$ converge together to infinity. If $m$ does n
ot grow too fast and if the draws are uniform, then the limiting shape is the same as the limiting spectrum of the GUE. In the non-uniform case, a control of both highest probabilities will ensure the convergence of the first row of the tableau toward the Tracy--Widom distribution.
We show that the equation of motion from the Dirac-Born-Infeld effective action of a general scalar field with some specific potentials admits exact solutions after appropriate field redefinitions. Based on the exact solutions and their energy-moment
um tensors, we find that massive scalars and massless scalars of oscillating modes in the DBI effective theory are not pressureless generically for any possible momenta, which implies that the pressureless tachyon matter forming at late time of the tachyon condensation process should not really be some massive matter. It is more likely that the tachyon field at late time behaves as a massless scalar of zero modes. At kinks, the tachyon can be viewed as a massless scalar of a translational zero mode describing a stable and static D-brane with one dimension lower. Near the vacuum, the tachyon in regions without the caustic singularities can be viewed as a massless scalar that has the same zero mode solution as a fundamental string moving with a critical velocity. We find supporting evidences to this conclusion by considering a DBI theory with modified tachyon potential, in which the development of caustics near the vacuum may be avoided.
Valiant-Vazirani showed in 1985 [VV85] that solving NP with the promise that yes instances have only one witness is powerful enough to solve the entire NP class (under randomized reductions). We are interested in extending this result to the quantu
m setting. We prove extensions to the classes Merlin-Arthur MA and Quantum-Classical-Merlin-Arthur QCMA. Our results have implications for the complexity of approximating the ground state energy of a quantum local Hamiltonian with a unique ground state and an inverse polynomial spectral gap. We show that the estimation (to within polynomial accuracy) of the ground state energy of poly-gapped 1-D local Hamiltonians is QCMA-hard [AN02], under randomized reductions. This is in stark contrast to the case of constant gapped 1-D Hamiltonians, which is in NP [Has07]. Moreover, it shows that unless QCMA can be reduced to NP by randomized reductions, there is no classical description of the ground state of every poly-gapped local Hamiltonian that allows efficient calculation of expectation values. Finally, we discuss a few of the obstacles to the establishment of an analogous result to the class Quantum-Merlin-Arthur (QMA). In particular, we show that random projections fail to provide a polynomial gap between two witnesses.
This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to students familia
r with just the fundamentals of algebraic topology.
It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well known principle of relativity of simultan
eity. The lack of a universal present implies the existence of past, present and future as a collection of events on a four dimensional manifold or continuum wherein three dimensions are space like and one dimension is time like. However, such a continuum precludes the possibility of evolution of future from the present as all events exist forever so to speak on the continuum with the tenses past, present and future merely being perceptions of different inertial frames. Such a far-reaching ontological concept, created by a mere convention, is yet to gain full acceptance. In this paper, we present arguments in favour of an absolute present, which means simultaneous events are simultaneous in all inertial frames, and subscribe to evolution of future from the present.
We consider parsimonious construction of empirical equations, to promote interest in them as a stepping-stone model to the physical law. To this end, we provide a variety of historical examples and simulate a parsimonious empirical calculation of Pla
nck law, and of van der Waals equation. Thereby we provide a) Empirical forms of Planck law, and b) Collation of verified symmetries and catastrophes-like properties of empirical P-T surface of real gases. An empirical equation of state for a real gas should take account of these properties.
