639 research outputs found
Entropy in quantum chromodynamics
We review the role of zero-temperature entropy in several closely-related
contexts in QCD. The first is entropy associated with disordered condensates,
including . The second is vacuum entropy arising from QCD
solitons such as center vortices, yielding confinement and chiral symmetry
breaking. The third is entanglement entropy, which is entropy associated with a
pure state, such as the QCD vacuum, when the state is partially unobserved and
unknown. Typically, entanglement entropy of an unobserved three-volume scales
not with the volume but with the area of its bounding surface. The fourth
manifestation of entropy in QCD is the configurational entropy of
light-particle world-lines and flux tubes; we argue that this entropy is
critical for understanding how confinement produces chiral symmetry breakdown,
as manifested by a dynamically-massive quark, a massless pion, and a condensate.Comment: 22 pages, 2 figures. Preprint version of invited review for Modern
Physics Letters
Entanglement and alpha entropies for a massive Dirac field in two dimensions
We present some exact results about universal quantities derived from the
local density matrix, for a free massive Dirac field in two dimensions. We
first find the trace of powers of the density matrix in a novel fashion, which
involves the correlators of suitable operators in the sine-Gordon model. These,
in turn, can be written exactly in terms of the solutions of non-linear
differential equations of the Painlev\'e V type. Equipped with the previous
results, we find the leading terms for the entanglement entropy, both for short
and long distances, and showing that in the intermediate regime it can be
expanded in a series of multiple integrals. The previous results have been
checked by direct numerical calculations on the lattice, finding perfect
agreement. Finally, we comment on a possible generalization of the entanglement
entropy c-theorem to the alpha-entropies.Comment: Clarification in section 2, one reference added. 15 pages, 3 figure
Entropy and Correlation Functions of a Driven Quantum Spin Chain
We present an exact solution for a quantum spin chain driven through its
critical points. Our approach is based on a many-body generalization of the
Landau-Zener transition theory, applied to fermionized spin Hamiltonian. The
resulting nonequilibrium state of the system, while being a pure quantum state,
has local properties of a mixed state characterized by finite entropy density
associated with Kibble-Zurek defects. The entropy, as well as the finite spin
correlation length, are functions of the rate of sweep through the critical
point. We analyze the anisotropic XY spin 1/2 model evolved with a full
many-body evolution operator. With the help of Toeplitz determinants calculus,
we obtain an exact form of correlation functions. The properties of the evolved
system undergo an abrupt change at a certain critical sweep rate, signaling
formation of ordered domains. We link this phenomenon to the behavior of
complex singularities of the Toeplitz generating function.Comment: 16 pgs, 7 fg
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
We consider the Renyi entanglement entropies in the one-dimensional XX
spin-chains with open boundary conditions in the presence of a magnetic field.
In the case of a semi-infinite system and a block starting from the boundary,
we derive rigorously the asymptotic behavior for large block sizes on the basis
of a recent mathematical theorem for the determinant of Toeplitz plus Hankel
matrices. We conjecture a generalized Fisher-Hartwig form for the corrections
to the asymptotic behavior of this determinant that allows the exact
characterization of the corrections to the scaling at order o(1/l) for any n.
By combining these results with conformal field theory arguments, we derive
exact expressions also in finite chains with open boundary conditions and in
the case when the block is detached from the boundary.Comment: 24 pages, 9 figure
Understanding the determinants of stability and folding of small globular proteins from their energetics
The results of minimal model calculations suggest that the stability and the
kinetic accessibility of the native state of small globular proteins are
controlled by few "hot" sites. By mean of molecular dynamics simulations around
the native conformation, which simulate the protein and the surrounding solvent
at full--atom level, we generate an energetic map of the equilibrium state of
the protein and simplify it with an Eigenvalue decomposition. The components of
the Eigenvector associated with the lowest Eigenvalue indicate which are the
"hot" sites responsible for the stability and for the fast folding of the
protein. Comparison of these predictions with the results of mutatgenesis
experiments, performed for five small proteins, provide an excellent agreement
- …