25,536 research outputs found
Asymptotic Freedom: From Paradox to Paradigm
Asymptotic freedom was developed as a response to two paradoxes: the
weirdness of quarks, and in particular their failure to radiate copiously when
struck; and the coexistence of special relativity and quantum theory, despite
the apparent singularity of quantum field theory. It resolved these paradoxes,
and catalyzed the development of several modern paradigms: the hard reality of
quarks and gluons, the origin of mass from energy, the simplicity of the early
universe, and the power of symmetry as a guide to physical law.Comment: 26 pages, 10 figures. Lecture on receipt of the 2004 Nobel Prize. v2:
typo (in Ohm's law) correcte
Graphical description of local Gaussian operations for continuous-variable weighted graph states
The form of a local Clifford (LC, also called local Gaussian (LG)) operation
for the continuous-variable (CV) weighted graph states is presented in this
paper, which is the counterpart of the LC operation of local complementation
for qubit graph states. The novel property of the CV weighted graph states is
shown, which can be expressed by the stabilizer formalism. It is distinctively
different from the qubit weighted graph states, which can not be expressed by
the stabilizer formalism. The corresponding graph rule, stated in purely graph
theoretical terms, is described, which completely characterizes the evolution
of CV weighted graph states under this LC operation. This LC operation may be
applied repeatedly on a CV weighted graph state, which can generate the
infinite LC equivalent graph states of this graph state. This work is an
important step to characterize the LC equivalence class of CV weighted graph
states.Comment: 5 pages, 6 figure
The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures
Microcanonical thermodynamics allows the application of statistical mechanics
both to finite and even small systems and also to the largest, self-gravitating
ones. However, one must reconsider the fundamental principles of statistical
mechanics especially its key quantity, entropy. Whereas in conventional
thermostatistics, the homogeneity and extensivity of the system and the
concavity of its entropy are central conditions, these fail for the systems
considered here. For example, at phase separation, the entropy, S(E), is
necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as
inhomogeneities and surface effects cannot be scaled away, one must be careful
with the standard arguments of splitting a system into two subsystems, or
bringing two systems into thermal contact with energy or particle exchange. Not
only the volume part of the entropy must be considered. As will be shown here,
when removing constraints in regions of a negative heat capacity, the system
may even relax under a flow of heat (energy) against a temperature slope. Thus
the Clausius formulation of the second law: ``Heat always flows from hot to
cold'', can be violated. Temperature is not a necessary or fundamental control
parameter of thermostatistics. However, the second law is still satisfied and
the total Boltzmann entropy increases. In the final sections of this paper, the
general microscopic mechanism leading to condensation and to the convexity of
the microcanonical entropy at phase separation is sketched. Also the
microscopic conditions for the existence (or non-existence) of a critical
end-point of the phase-separation are discussed. This is explained for the
liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of
Chemical Physic
An Exact Prediction of N=4 SUSYM Theory for String Theory
We propose that the expectation value of a circular BPS-Wilson loop in N=4
SUSYM can be calculated exactly, to all orders in a 1/N expansion and to all
orders in g^2 N. Using the AdS/CFT duality, this result yields a prediction of
the value of the string amplitude with a circular boundary to all orders in
alpha' and to all orders in g_s. We then compare this result with string
theory. We find that the gauge theory calculation, for large g^2 N and to all
orders in the 1/N^2 expansion does agree with the leading string theory
calculation, to all orders in g_s and to lowest order in alpha'. We also find a
relation between the expectation value of any closed smooth Wilson loop and the
loop related to it by an inversion that takes a point along the loop to
infinity, and compare this result, again successfully, with string theory.Comment: LaTeX, 22 pages, 3 figures. Argument corrected and two new sections
adde
Star Algebra Spectroscopy
The spectrum of the infinite dimensional Neumann matrices M^{11}, M^{12} and
M^{21} in the oscillator construction of the three-string vertex determines key
properties of the star product and of wedge and sliver states. We study the
spectrum of eigenvalues and eigenvectors of these matrices using the derivation
K_1 = L_1 + L_{-1} of the star algebra, which defines a simple infinite matrix
commuting with the Neumann matrices. By an exact calculation of the spectrum of
K_1, and by consideration of an operator generating wedge states, we are able
to find analytic expressions for the eigenvalues and eigenvectors of the
Neumann matrices and for the spectral density. The spectrum of M^{11} is
continuous in the range [-1/3, 0) with degenerate twist even and twist odd
eigenvectors for every eigenvalue except for -1/3.Comment: LaTeX, 30 pages, 2 figure
- …