Exercises in Statistical Mechanics

... Reσ(ω) = kB T 0 (c) Write the Diffusion constant D in terms of the velocity-velocity correlation function, assuming that this correlation has a finite range in time. Use Kubo’s formula from (b) in the DC limit of zero frequency to derive the Einstein-Nernst formula for the σ mobility µ = ne = eD/kB ...

... Reσ(ω) = kB T 0 (c) Write the Diffusion constant D in terms of the velocity-velocity correlation function, assuming that this correlation has a finite range in time. Use Kubo’s formula from (b) in the DC limit of zero frequency to derive the Einstein-Nernst formula for the σ mobility µ = ne = eD/kB ...

Problem set 7

... Problem set 7 Due by beginning of class on Monday Mar 5, 2012 BCH formula for x and p , SHO 1. Consider the function f (t) = etA Be−tA where A, B are a pair of operators (e.g. position and momentum or creation and annihilation operators etc.). t is a parameter which could be a time interval or a spa ...

... Problem set 7 Due by beginning of class on Monday Mar 5, 2012 BCH formula for x and p , SHO 1. Consider the function f (t) = etA Be−tA where A, B are a pair of operators (e.g. position and momentum or creation and annihilation operators etc.). t is a parameter which could be a time interval or a spa ...

Kant and Kantianism

... First Formula: Universal Law: 1. The Formula of Universal Law/Formula of Universal Law of Nature: – "Act only according to that maxim whereby you can at the same time will that it should become a universal law." – "Act as if the maxim of your action were to become through your will a universal law ...

... First Formula: Universal Law: 1. The Formula of Universal Law/Formula of Universal Law of Nature: – "Act only according to that maxim whereby you can at the same time will that it should become a universal law." – "Act as if the maxim of your action were to become through your will a universal law ...

Planck`s Law and Light Quantum Hypothesis.

... that is, the relation between the radiation density and the mean energy of an oscillator, and they make assumptions about the number of degrees of freedom of the ether, which appear in the above formula (the first factor on the right– hand side). This factor, however, can be derived only from classi ...

... that is, the relation between the radiation density and the mean energy of an oscillator, and they make assumptions about the number of degrees of freedom of the ether, which appear in the above formula (the first factor on the right– hand side). This factor, however, can be derived only from classi ...

A path towards quantum gravity

... History of singularity theorems • Penrose: singularities in gravitational collapse • Hawking, Geroch, Hawking—Ellis, HAWKINGPENROSE, Kriele: spacetime singularities are generic properties of GR, provided that energy conditions hold. Very little use of the Einstein equations is made. Key role of top ...

... History of singularity theorems • Penrose: singularities in gravitational collapse • Hawking, Geroch, Hawking—Ellis, HAWKINGPENROSE, Kriele: spacetime singularities are generic properties of GR, provided that energy conditions hold. Very little use of the Einstein equations is made. Key role of top ...

Relativity + Quantum + Gravity

... • These three concepts are the basis of physics. • They contain the three fundamental constants c,ħ,G , which form a complete system of units. • Are these concepts compatible with each other? - Relativity and gravity (= general relativity) are designed to be compatible. - Relativity and quantum phys ...

... • These three concepts are the basis of physics. • They contain the three fundamental constants c,ħ,G , which form a complete system of units. • Are these concepts compatible with each other? - Relativity and gravity (= general relativity) are designed to be compatible. - Relativity and quantum phys ...

Quantum Mechanical Derivation of the Wallis Formula for $\ pi$

... was derived by John Wallis in 1655 [1] (see also [2]) by a method of successive interpolations. While several mathematical proofs of this formula have been put forth in the past (many just in the last decade) using probability [3], combinatorics and probability [4], geometric means [5], trigonometry ...

... was derived by John Wallis in 1655 [1] (see also [2]) by a method of successive interpolations. While several mathematical proofs of this formula have been put forth in the past (many just in the last decade) using probability [3], combinatorics and probability [4], geometric means [5], trigonometry ...

Program - LQG

... We will present a general mechanism for the emergence of an effective classical spacetime from a fundamental theory of quantum cosmology coupled to matter. This idea is based on QFT on quantum spacetime, and the emergent classical metric is not just the naïve expectation value of a ``metric operator ...

... We will present a general mechanism for the emergence of an effective classical spacetime from a fundamental theory of quantum cosmology coupled to matter. This idea is based on QFT on quantum spacetime, and the emergent classical metric is not just the naïve expectation value of a ``metric operator ...

Lecture

... Asymptotic freedom: g(m) runs to 0 when m grows GR is perturbatively non-renormalisable: no running gravity coupling G(m) Maybe nevertheless ...

... Asymptotic freedom: g(m) runs to 0 when m grows GR is perturbatively non-renormalisable: no running gravity coupling G(m) Maybe nevertheless ...

Key ideas that led to QED vacuum consists of "sea of electrons

... • In fact, the theory becomes trivial, which raises question about the perturbation results; • Yet, there is not a single non-trivial QFT in 3+1 dimensions that can be analyzed nonperturbatively; ...

... • In fact, the theory becomes trivial, which raises question about the perturbation results; • Yet, there is not a single non-trivial QFT in 3+1 dimensions that can be analyzed nonperturbatively; ...

Aalborg Universitet The Landauer-Büttiker formula and resonant quantum transport

... The gαβ (T, µ, η, N ) are the conductance coefficients [3]. It is clear from the above formula that we work in the linear response regime. Below we are going to take the limit N → ∞, followed by the limit η → 0. The limits have to be taken in this order, since the error term is in fact O(V 2 /η 2 ). ...

... The gαβ (T, µ, η, N ) are the conductance coefficients [3]. It is clear from the above formula that we work in the linear response regime. Below we are going to take the limit N → ∞, followed by the limit η → 0. The limits have to be taken in this order, since the error term is in fact O(V 2 /η 2 ). ...

What is Entanglement? Entangled Fields Looking at Entangled

... cannot really be considered as separate objects, but are intrinsically connected or “entangled” with each other. For example, performing a measurement on one, such as measuring the particles spin as in the diagram above, instantaneously affects the result of measuring the other. This phenomena occur ...

... cannot really be considered as separate objects, but are intrinsically connected or “entangled” with each other. For example, performing a measurement on one, such as measuring the particles spin as in the diagram above, instantaneously affects the result of measuring the other. This phenomena occur ...

Abstracts of the talks

... the same genus need not be equivalent, but one can show that there are only finitely many equivalence classes of quadratic forms within a genus. In fact, there is an explicit formula for the number of equivalence classes of quadratic forms in the genus of a fixed quadratic form q (counted with multi ...

... the same genus need not be equivalent, but one can show that there are only finitely many equivalence classes of quadratic forms within a genus. In fact, there is an explicit formula for the number of equivalence classes of quadratic forms in the genus of a fixed quadratic form q (counted with multi ...

TALK - ECM

... provided by all modes with wave number k' > k The dynamics of the relevant mode is obtained by tracing over the environment. This generally leaves the relevant mode in a mixed state, whose evolution is determined by a Feynman-Vernon influence functional (IF) ...

... provided by all modes with wave number k' > k The dynamics of the relevant mode is obtained by tracing over the environment. This generally leaves the relevant mode in a mixed state, whose evolution is determined by a Feynman-Vernon influence functional (IF) ...

Large N quantum system

... • Problem Infinite number of solutions. • f like a Nambu-Goldstone boson. • Fix: Remember that the symmetry is also explicitly broken (like the pion mass). ...

... • Problem Infinite number of solutions. • f like a Nambu-Goldstone boson. • Fix: Remember that the symmetry is also explicitly broken (like the pion mass). ...

Daniel Heineman Prize: The Quest for Quantum Gravity

... gravity, in light-cone gauge. In fact, it is the full Hamiltonian for M theory, with boundary condition of flat spacetime with a null circle ...

... gravity, in light-cone gauge. In fact, it is the full Hamiltonian for M theory, with boundary condition of flat spacetime with a null circle ...

Quantum Fields in Curved Spacetime

... • The next order subtracts the constant in D0: the contribution to the effective action diverges at both small s and large s • This term modifies the IR so it is not a local term in the IR. • It is wrong to subtract it. ...

... • The next order subtracts the constant in D0: the contribution to the effective action diverges at both small s and large s • This term modifies the IR so it is not a local term in the IR. • It is wrong to subtract it. ...

Clément Hongler Spring 2016 Lecture Series EPFL

... conjectural, major recent progress in the field of rigorous conformal invariance allows one to make mathematical sense of much of the story: In particular, for the Ising model we are close to reaching a complete understanding of how it works. The series will thus focus on giving an intuitive underst ...

... conjectural, major recent progress in the field of rigorous conformal invariance allows one to make mathematical sense of much of the story: In particular, for the Ising model we are close to reaching a complete understanding of how it works. The series will thus focus on giving an intuitive underst ...

The Asymptotic Safety Scenario for Quantum Gravity Bachelor

... less than the energy needed to probe these effects. The standard approach of quantizing gravity in a perturbative quantum field theoretical framework using Feynman graphs and the spin two graviton as its force carrier is plagued by many non renormalizable ultraviolet divergences. It is however possi ...

... less than the energy needed to probe these effects. The standard approach of quantizing gravity in a perturbative quantum field theoretical framework using Feynman graphs and the spin two graviton as its force carrier is plagued by many non renormalizable ultraviolet divergences. It is however possi ...

" Quantum gravity": an oxymoron

... The innumerable and learned efforts during seventy years to create a quantum formulation of general relativity have only beaten the air – et pour cause, as we shall see. On the other hand, it is evident to any unprejudiced scientist that definite reasons must be at the root of this failure. First of ...

... The innumerable and learned efforts during seventy years to create a quantum formulation of general relativity have only beaten the air – et pour cause, as we shall see. On the other hand, it is evident to any unprejudiced scientist that definite reasons must be at the root of this failure. First of ...

Bilbao - INFN - Sezione di Firenze

... framework into something predictive ... and testable. Many unresolved puzzles in gravitation and cosmology (big bang, black holes, cosm..) probably do need a consistent way to combine GR and QM Insisting on theoretical consistency has paid off enormously towards understanding EW and Strong interact ...

... framework into something predictive ... and testable. Many unresolved puzzles in gravitation and cosmology (big bang, black holes, cosm..) probably do need a consistent way to combine GR and QM Insisting on theoretical consistency has paid off enormously towards understanding EW and Strong interact ...

universality

... microscopic theories : where the laws are formulated effective theories : where observations are made effective theory may involve different degrees of freedom as compared to microscopic theory example: microscopic theory only for fermionic atoms , macroscopic theory involves bosonic collective degr ...

... microscopic theories : where the laws are formulated effective theories : where observations are made effective theory may involve different degrees of freedom as compared to microscopic theory example: microscopic theory only for fermionic atoms , macroscopic theory involves bosonic collective degr ...

Physics 120 Homework Set #1 (due Sunday

... 6) In the “Illusion of Gravity” article, the author states: “A quantum theory of gravity will probably provide us with an entirely new perspective of what spacetime is.” Also, “if matter obeys the laws of quantum mechanics and gravity obeys the laws of general relativity, we end up with mathematical ...

... 6) In the “Illusion of Gravity” article, the author states: “A quantum theory of gravity will probably provide us with an entirely new perspective of what spacetime is.” Also, “if matter obeys the laws of quantum mechanics and gravity obeys the laws of general relativity, we end up with mathematical ...