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Thermalisation of Quantum States
D. C. Brody, L. P. Hughston
An exact stochastic model for the thermalisation of quantum states is proposed. The model has various physically appealing properties. The dynamics are characterised by an underlyi…
On the Symmetry of Real-Space Renormalisation
D. C. Brody, A. Ritz
A natural geometry, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is used to study the symmetry properties of r…
The Quantum Canonical Ensemble
D. C. Brody, L. P. Hughston
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic…
Geometrisation of Statistical Mechanics
Dorje C. Brody, Lane P. Hughston
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing…
Restoration of Isotropy for Spin Models
D. C. Brody, A. Ritz
Using real-space renormalisation techniques we analyse the Ising model on a Sierpiński gasket with anisotropic microscopic couplings, and observe a restoration of isotropy on macro…
Generalised Heisenberg Relations
Dorje C. Brody, Lane P. Hughston
A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of…
Geometry of Thermodynamic States
Dorje C. Brody, Lane P. Hughston
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equ…
Statistical Geometry in Quantum Mechanics
Dorje C. Brody, Lane P. Hughston
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical pro…