14,568 research outputs found
Group Cohomology, Modular Theory and Space-time Symmetries
The Bisognano-Wichmann property on the geometric behavior of the modular
group of the von Neumann algebras of local observables associated to wedge
regions in Quantum Field Theory is shown to provide an intrinsic sufficient
criterion for the existence of a covariant action of the (universal covering
of) the Poincar\'e group. In particular this gives, together with our previous
results, an intrinsic characterization of positive-energy conformal
pre-cosheaves of von Neumann algebras. To this end we adapt to our use Moore
theory of central extensions of locally compact groups by polish groups,
selecting and making an analysis of a wider class of extensions with natural
measurable properties and showing henceforth that the universal covering of the
Poincar\'e group has only trivial central extensions (vanishing of the first
and second order cohomology) within our class.Comment: 18 pages, plain TeX, preprint Roma Tor vergata n. 20 dec. 9
Selfishness Level of Strategic Games
We introduce a new measure of the discrepancy in strategic games between the
social welfare in a Nash equilibrium and in a social optimum, that we call
selfishness level. It is the smallest fraction of the social welfare that needs
to be offered to each player to achieve that a social optimum is realized in a
pure Nash equilibrium. The selfishness level is unrelated to the price of
stability and the price of anarchy and is invariant under positive linear
transformations of the payoff functions. Also, it naturally applies to other
solution concepts and other forms of games.
We study the selfishness level of several well-known strategic games. This
allows us to quantify the implicit tension within a game between players'
individual interests and the impact of their decisions on the society as a
whole. Our analyses reveal that the selfishness level often provides a deeper
understanding of the characteristics of the underlying game that influence the
players' willingness to cooperate.
In particular, the selfishness level of finite ordinal potential games is
finite, while that of weakly acyclic games can be infinite. We derive explicit
bounds on the selfishness level of fair cost sharing games and linear
congestion games, which depend on specific parameters of the underlying game
but are independent of the number of players. Further, we show that the
selfishness level of the -players Prisoner's Dilemma is ,
where and are the benefit and cost for cooperation, respectively, that
of the -players public goods game is , where is
the public good multiplier, and that of the Traveler's Dilemma game is
, where is the bonus. Finally, the selfishness level of
Cournot competition (an example of an infinite ordinal potential game, Tragedy
of the Commons, and Bertrand competition is infinite.Comment: 34 page
Dispersive readout of valley splittings in cavity-coupled silicon quantum dots
The bandstructure of bulk silicon has a six-fold valley degeneracy. Strain in
the Si/SiGe quantum well system partially lifts the valley degeneracy, but the
materials factors that set the splitting of the two lowest lying valleys are
still under intense investigation. We propose a method for accurately
determining the valley splitting in Si/SiGe double quantum dots embedded into a
superconducting microwave resonator. We show that low lying valley states in
the double quantum dot energy level spectrum lead to readily observable
features in the cavity transmission. These features generate a "fingerprint" of
the microscopic energy level structure of a semiconductor double quantum dot,
providing useful information on valley splittings and intervalley coupling
rates.Comment: 8 pages, 4 figure
Effective time-reversal symmetry breaking in the spin relaxation in a graphene quantum dot
We study the relaxation of a single electron spin in a circular gate-tunbable
quantum dot in gapped graphene. Direct coupling of the electron spin to
out-of-plane phonons via the intrinsic spin-orbit coupling leads to a
relaxation time T_1 which is independent of the B-field at low fields. We also
find that Rashba spin-orbit induced admixture of opposite spin states in
combination with the emission of in-plane phonons provides various further
relaxation channels via deformation potential and bond-length change. In the
absence of valley mixing, spin relaxation takes place within each valley
separately and thus time-reversal symmetry is effectively broken, thus
inhibiting the van Vleck cancellation at B=0 known from GaAs quantum dots. Both
the absence of the van Vleck cancellation as well as the out-of-plane phonons
lead to a behavior of the spin relaxation rate at low magnetic fields which is
markedly different from the known results for GaAs. For low B-fields, we find
that the rate is constant in B and then crosses over to ~B^2 or ~B^4 at higher
fields.Comment: 5 pages, 2 figures, 1 tabl
Modular localization and Wigner particles
We propose a framework for the free field construction of algebras of local
observables which uses as an input the Bisognano-Wichmann relations and a
representation of the Poincare' group on the one-particle Hilbert space. The
abstract real Hilbert subspace version of the Tomita-Takesaki theory enables us
to bypass some limitations of the Wigner formalism by introducing an intrinsic
spacetime localization. Our approach works also for continuous spin
representations to which we associate a net of von Neumann algebras on
spacelike cones with the Reeh-Schlieder property. The positivity of the energy
in the representation turns out to be equivalent to the isotony of the net, in
the spirit of Borchers theorem. Our procedure extends to other spacetimes
homogeneous under a group of geometric transformations as in the case of
conformal symmetries and de Sitter spacetime.Comment: 22 pages, LaTeX. Some errors have been corrected. To appear on Rev.
Math. Phy
Ratcheted molecular-dynamics simulations identify efficiently the transition state of protein folding
The atomistic characterization of the transition state is a fundamental step
to improve the understanding of the folding mechanism and the function of
proteins. From a computational point of view, the identification of the
conformations that build out the transition state is particularly cumbersome,
mainly because of the large computational cost of generating a
statistically-sound set of folding trajectories. Here we show that a biasing
algorithm, based on the physics of the ratchet-and-pawl, can be used to
identify efficiently the transition state. The basic idea is that the
algorithmic ratchet exerts a force on the protein when it is climbing the
free-energy barrier, while it is inactive when it is descending. The transition
state can be identified as the point of the trajectory where the ratchet
changes regime. Besides discussing this strategy in general terms, we test it
within a protein model whose transition state can be studied independently by
plain molecular dynamics simulations. Finally, we show its power in
explicit-solvent simulations, obtaining and characterizing a set of
transition--state conformations for ACBP and CI2
On a conjecture regarding Fisher information
Fisher's information measure plays a very important role in diverse areas of
theoretical physics. The associated measures as functionals of quantum
probability distributions defined in, respectively, coordinate and momentum
spaces, are the protagonists of our present considerations. The product of them
has been conjectured to exhibit a non trivial lower bound in [Phys. Rev. A
(2000) 62 012107]. We show here that such is not the case. This is illustrated,
in particular, for pure states that are solutions to the free-particle
Schr\"odinger equation. In fact, we construct a family of counterexamples to
the conjecture, corresponding to time-dependent solutions of the free-particle
Schr\"odinger equation. We also give a new conjecture regarding any
normalizable time-dependent solution of this equation.Comment: 4 pages; revised equations, results unchange
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