2,510 research outputs found
Clustering of fermionic truncated expectation values via functional integration
I give a simple proof that the correlation functions of many-fermion systems
have a convergent functional Grassmann integral representation, and use this
representation to show that the cumulants of fermionic quantum statistical
mechanics satisfy l^1-clustering estimates
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
Science, Technology, and Medicine have Progressed Immensely during the Last Five Centuries, yet Mankind Is Threatened by Self-Destruction
During the last 5900 years, creative human minds have dispelled false beliefs about our universe, as well as chemical, physical, and biomedical phenomena. Life expectancies in most inhabited parts of our world have increased appreciably. A brief survey of those who contributed to the progress of science, technology, and understanding is presented. Yet, primitive instincts and ambitions still dominate our world, and conflicts threaten to destroy life on this planet by way of nuclear weapons. Societies are ruled by politicians and militaries, for scientists are “on tap, but not on top”. The contrast between reason-based progress and instinct-based aggression is mind-boggling
Cyclic Diamondoid Structures with Shared Vertices, Edges, or 6-membered Rings
Diamondoid structures with shared vertices, edges, or 6-membered rings can theoretically be
curved into toroidal structures whose calculated energy provides information about steric strain.
Diamondoid hydrocarbons sharing one vertex between two adamantane units are called [n]spiromantanes,
where n indicates the number of adamantane units. When a pair of adamantane units shares one CC bond,
the resulting assembly is called one-edge-[n]mantane, specifying (by letters in square brackets) which
bonds are shared by the adamantane units. Two adjacent edges may be shared by a pair of adamantane
units, and the assembly is called two-edge-[n]mantane, again specifying by letters in square brackets the
shared bonds. Catamantanes or perimantanes sharing a 6-membered ring of carbon atoms may form larger
rings in an assembly which is called [n]cyclomantane; in the case of catamantanes, the structure of the
diamondoid is specified by codes of the dualists. Finally, nanotubes derived from hexagonal diamond, as
well as corresponding toroidal structures, are discussed
A Criterion for the Critical Number of Fermions and Chiral Symmetry Breaking in Anisotropic QED(2+1)
By analyzing the strength of a photon-fermion coupling using basic scattering
processes we calculate the effect of a velocity anisotropy on the critical
number of fermions at which mass is dynamically generated in planar QED. This
gives a quantitative criterion which can be used to locate a quantum critical
point at which fermions are gapped and confined out of the physical spectrum in
a phase diagram of various condensed matter systems. We also discuss the
mechanism of relativity restoration within the symmetric, quantum-critical
phase of the theory.Comment: To appear in Physical Review
A simple mathematical model for the effect of benzoannelation on cyclic conjugation
In a series of earlier studies, it was established that benzoannelation in the angular (resp. linear) position relative to a ring R of a polycyclic conjugated π-electron system, increases (resp. decreases) the intensity of the cyclic conjugation in the ring R. Herein, it is shown how this regularity can be explained by means of a simple, Kekulé-structurebased argument, itself based on an idea of Randić from the 1970s
Chemical Graphs. XL.1 Three Relations Between the Fibonacci Sequence and the Numbers of Kekule Structures for Non-branched cata-Condensed Polycyclic Aromatic Hydrocarbons
Fo·r benze.notd or non-benzenoid ca:ta1fusenes having a non-
ibranched string 01f cata-co.ndensed rings, the numbers K of
Kekule structures (perfect matching·s) can be expressed vi<t
the recurrence relationship (1); as a coa.-ollary when each annelated
.segment has exactly two ring.s, the numbers O\u27f Kelm.le
structures form the Fiibonacci sequence.
Coro.nary 2 presents a second re.lationshi:p with Fiibonacci
numbers. Algebraic expressions for the number of Kekule struc-
1tures in non-brainched cata.fusenes 1n terms of hexago.n numbers
iJn each linearly condensed segment can be obtained. The
numbers of terms in .such .a,,lgebraic expressivns lead to a new
numerical triangle (Table I) which is related to Pascal\u27s triangle,
and which pwvides a third link with the F ~bonacci
numbers expressed either by relation (7) or by the equivalent
relation (10)
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