Phase Space Craziness
This famous theorem states that every continuous symmetry of a physical system corresponds to a conserved quantity.
What is Noether’s theorem?
In the canonical ensemble, the partition function is related to this thermodynamic potential.
What is the Helmholtz free energy?
In relativistic electrodynamics, this quantity combines the electric and magnetic potential into a single object that transforms as a Lorentz 4-vector.
What is a four-potential?
In the Monte Carlo method, the result is estimated by sampling from a probability distribution based on this principle.
What is the law of large numbers?
This physicist introduced the concept of gauge symmetry in his 1918 work, laying the foundation for modern gauge theories in particle physics.
Who is Hermann Weyl?
In the context of Hamiltonian mechanics, these are the two types of variables that define phase space.
What are generalized coordinates and generalized momenta?
The large deviation function describes the probability of deviations from equilibrium behavior. In thermodynamics, it corresponds to this fundamental concept.
What is the entropy function?
This effect, predicted by general relativity, was confirmed during the 1919 solar eclipse by Arthur Eddington.
This function, named after a British mathematician, solves inhomogeneous differential equations by representing a system’s impulse response.
What is the Green's function?
The Ehrenfest theorem connects quantum mechanics to classical mechanics by showing that the expectation values of operators obey equations analogous to these classical laws.
What are Hamilton’s equations?
In a double pendulum, small perturbations in initial conditions lead to drastically different outcomes. This is a signature of what kind of system?
What is a chaotic system?
This thorem relates fluctuations in a system to its response to perturbations, connecting microscopic reversibility with macroscopic irreversibility.
What is the fluctuation-dissipation theorem?
In electrodynamics, in systems where the electric dipole moment does not change in time, this type of radiation becomes the leading-order term.
What is magnetic dipole or electric quadrupole radiation?
The action of a differential operator on a function can often be expressed using this integral transform, which is widely used in signal processing and quantum mechanics.
What is the Fourier transform?
In 1908, this physicist proposed an early quantum theory of blackbody radiation based on quantized harmonic oscillators, preceding Planck’s full theory.
Who is Paul Ehrenfest?
This fundamental theorem states that the volume of a set of states in phase space remains constant as the states evolve.
What is Liouville's theorem?
The Jarzynski equality relates equilibrium free energy differences to the exponential average of this thermodynamic quantity.
What is work?
In general relativity, energy conservation is often discussed in terms of this locally conserved quantity, which describes energy and momentum flow in spacetime.
What is the stress-energy tensor?
In functional analysis, a Hilbert space is a complete inner product space. What property makes it “complete”?
What is the convergence of Cauchy sequences?
This 19th-century theoretical framework explained the null result of the Michelson-Morley experiment through a contraction hypothesis, preserving the aether until Einstein’s relativity rendered it obsolete.
What is the Lorentz ether theory?
This dimensionless metric (symbolized by λ) quantifies the rate at which nearby trajectories in phase space diverge and is positive for chaotic systems.
What is the Lyapunov exponent?
The Onsager reciprocal relations arise from microscopic time reversibility and impose constraints on these types of coefficients.
What are transport coefficients?
The Liénard–Wiechert potentials describe the electromagnetic fields produced by a moving charge, leading to this type of radiation emitted by accelerating charges.
What is synchotron radiation?
This mathematical mapping converts spin-1/2 operators on a one-dimensional quantum spin system into fermionic creation and annihilation operators.
What is the Jordan-Wigner transform?
The Thorne-Hawking-Preskill bet was a famous wager about the fate of information in this physical process.
What is black hole evaporation?