65 research outputs found
Quantum mechanical rules for observed observers and the consistency of quantum theory
No full textI argue that the rules of unitary quantum mechanics imply that observers who
will themselves be subject to measurements in a linear combination of
macroscopic states (``cat" measurements) cannot make reliable predictions on
the results of experiments performed after such measurements. This lifts the
inconsistency in the interpretation of quantum mechanics recently identified by
Frauchiger and Renner. The Born rules for calculating the probability of
outcomes and for communicating with other observers do not generally apply for
cat-measured observers, nor can they generally be amended to incorporate
upcoming cat measurements. Quantum mechanical rules completed with these
conditions become fully consistent.Comment: Substantially expanded version published in Nature Communications; 15
pages, no figure
Composition of many spins, random walks and statistics
No full textAbstractThe multiplicities of the decomposition of the product of an arbitrary number n of spin s states into irreducible SU(2) representations are computed. Two complementary methods are presented, one based on random walks in representation space and another based on the partition function of the system in the presence of a magnetic field. The large-n scaling limit of these multiplicities is derived, including nonperturbative corrections, and related to semiclassical features of the system. A physical application of these results to ferromagnetism is explicitly worked out. Generalizations involving several types of spins, as well as spin distributions, are also presented. The corresponding problem for (anti-)symmetric composition of spins is also considered and shown to obey remarkable duality and bosonization relations and exhibit novel large-n scaling properties
Lattice Integrable Systems of the Haldane-Shastry Type
No full textWe present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interaction limit of the Sutherland system of particles with internal degrees of freedom and identifying the same limit in a corresponding Calogero system. The commuting integrals of motion of this system are found using the exchange operator formalism.We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interaction limit of the Sutherland system of particles with internal degrees of freedom and identifying the same limit in a corresponding Calogero system. The commuting integrals of motion of this system are found using the exchange operator formalism
Exclusion statistics and lattice random walks
No full textWe establish a connection between exclusion statistics with arbitrary integer exclusion parameter and a class of random walks on planar lattices. This connection maps the generating function for the number of closed walks of given length enclosing a given algebraic area on the lattice to the grand partition function of particles obeying exclusion statistics in a particular single-particle spectrum, determined by the properties of the random walk. Square lattice random walks, described in terms of the Hofstadter Hamiltonian, correspond to . In the case we explicitly construct a corresponding chiral random walk model on a triangular lattice, and we point to potential random walk models for higher . In this context, we also derive the form of the microscopic cluster coefficients for arbitrary exclusion statistics
Algebraic area enumeration for open lattice walks
No full textWe calculate the number of open walks of fixed length and algebraic area on a
square planar lattice by an extension of the operator method used for the
enumeration of closed walks. The open walk area is defined by closing the walks
with a straight line across their endpoints and can assume half-integer values
in lattice cell units. We also derive the length and area counting of walks
with endpoints on specific straight lines and outline an approach for dealing
with walks with fully fixed endpoints.Comment: 15 pages, 2 figure
Ferromagnets from higher SU(N) representations
No full textWe present a general formalism for deriving the thermodynamics of ferromagnets consisting of “atoms” carrying an arbitrary irreducible representation of SU(N) and coupled through long-range two-body quadratic interactions. Using this formalism, we derive the thermodynamics and phase structure of ferromagnets with atoms in the doubly symmetric or doubly antisymmetric irreducible representations. The symmetric representation leads to a paramagnetic and a ferromagnetic phase with transitions similar to the ones for the fundamental representation studied before. The antisymmetric representation presents qualitatively new features, leading to a paramagnetic and two distinct ferromagnetic phases that can coexist over a range of temperatures, two of them becoming metastable. Our results are relevant to magnetic systems of atoms with reduced symmetry in their interactions compared to the fundamental case. © 2025 The Author(s
Anomalous Quantum Mumbers and Topological Properties of Field Theories
No full textWe examine the connection between anomalous quantum numbers, symmetry breaking patterns and topological properties of some field theories. The main results are the following: In three dimensions the vacuum in the presence of abelian magnetic field configurations behaves like a superconductor. Its quantum numbers are exactly calculable and are connected with the Atiyah-Patodi-Singer index theorem. Boundary conditions, however, play a nontrivial role in this case. Local conditions were found to be physically preferable than the usual global ones. Due to topological reasons, only theories for which the gauge invariant photon mass in three dimensions obeys a quantization condition can support states of nonzero magnetic flux. For similar reasons, this mass induces anomalous angular momentum quantum numbers to the states of the theory. Parity invariance and global flavor symmetry were shown to be incompatible in such theories. In the presence of massless flavored fermions, parity will always break for an odd number of fermion flavors, while for even fermion flavors it may not break but only at the expense of maximally breaking the flavor symmetry. Finally, a connection between these theories and the quantum Hall effectwas indicated.</p
Inclusion statistics and particle condensation in 2 dimensions
No full textWe propose a new type of quantum statistics, which we call inclusion
statistics, in which particles tend to coalesce more than ordinary bosons.
Inclusion statistics is defined in analogy with exclusion statistics, in which
statistical exclusion is stronger than in Fermi statistics, but now
extrapolating beyond Bose statistics, resulting in statistical inclusion. A
consequence of inclusion statistics is that the lowest space dimension in which
particles can condense in the absence of potentials is , unlike for
the usual Bose-Einstein condensation. This reduction in the dimension happens
for any inclusion stronger than bosons, and the critical temperature increases
with stronger inclusion. Possible physical realizations of inclusion statistics
involving attractive interactions between bosons may be experimentally
achievable.Comment: 12 pages, 0 figur
Mapping the Calogero model on the Anyon model
No full textInternational audienceWe explicitly map the N -body one dimensional Calogero eigenstates in a harmonic well to the lowest Landau level sector of N -body eigenstates of the two dimensional anyon model in a harmonic well. The mapping is achieved in terms of a convolution kernel that uses as input the scattering eigenstates of the free Calogero model on the infinite line, which are obtained in an operator formulation
Ferromagnetic phase transitions in
No full textWe study the thermodynamics of a non-abelian ferromagnet consisting of “atoms” each carrying a fundamental representation of SU(N), coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global SU(N)-invariant states to magnetized ones breaking global invariance to SU(N−1)×U(1). Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual SU(2) ferromagnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model.We study the thermodynamics of a non-abelian ferromagnet consisting of "atoms" each carrying a fundamental representation of , coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global -invariant states to magnetized ones breaking global invariance to . Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual ferromagnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model
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