Note on the law of sargent

Uhlenbeck, G. E.; Kuiper, H.

doi:10.1016/s0031-8914(37)80105-6

Cited by 39 publications

(13 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The connection between scattering data and ρ(E) as noticed in [3,8] is briefly repeated here for clarity. While calculating the virial coefficients in the equation of an ideal gas, Beth and Uhlenbeck [9] found that the difference between the density of states (of scattered particles) with the interaction dn l (E)/dE and without dn…”

Section: Density Of Statesmentioning

confidence: 99%

No classical limit of quantum decay for broad states

Kelkar¹,

Nowakowski²

2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the σ meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances.

show abstract

Section: Density Of Statesmentioning

confidence: 99%

No classical limit of quantum decay for broad states

Kelkar¹,

Nowakowski²

2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…Beth and Uhlenbeck [33] (the derivation of their result is reproduced in [34], see also [35,36]) found that the difference between the density of states with interaction, n l , and without, n (0) l , is given by the derivative of the scattering phase shift δ l as,…”

Section: Statistical Physics Based Approachmentioning

confidence: 99%

Quantum decay law: critical times and the equivalence of approaches

Jiménez¹,

Kelkar²

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

Methods based on the use of Green's functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock-Krylov amplitude in terms of the coefficients introduced in the Green's functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective to understand the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, t c , from the exponential to the inverse power law behaviour at large times. Evaluating τ c = Γt c for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.

show abstract

“…For example, for (a/λ) = 2, convergence is obtained only when the sum extends to l max = 33. 4 This may be understood by noting that for small β (high temperature), the damping of the integrand from the Gaussian is less effective, and higher values of the variable k are needed for the convergence. From impact parameter argument [10], the cut-off l max (ka) in the sum over l therefore also increases.…”

Section: Numerical Comparisonmentioning

confidence: 99%

“…For a dilute gas at high temperature, it is the second virial coefficient that gives the dominant contribution. The second virial coefficient may also be calculated quantum mechanically from the Beth-Uhlenbeck formula using the hard-sphere scattering phase shifts in the various partial waves [4]. Contrary to naive expectations, the quantum result for the interaction energy of the Boltzmann gas at high temperatures is substantially different from the classical one, even when the thermal wavelength is only a fraction of the hard-sphere diameter.…”

Section: Introductionmentioning

confidence: 98%

Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas

2006

View full text Add to dashboard Cite

Abstract. Quantum effects in statistical mechanics are important when the thermal wavelength is of the order of, or greater than, the mean interatomic spacing. This is examined at depth taking the example of a hard-sphere Boltzmann gas. Using the virial expansion for the equation of state, it is shown that the interaction energy of a classical hard-sphere gas is exactly zero. When the (second) virial coefficient of such a gas is obtained quantum mechanically, however, the quantum contribution to the interaction energy is shown to be substantial. The importance of the semiclassical corrections to the interaction energy shows up dramatically in such a system. Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas 2

show abstract

Note on the law of sargent

Cited by 39 publications

References 8 publications

No classical limit of quantum decay for broad states

No classical limit of quantum decay for broad states

Quantum decay law: critical times and the equivalence of approaches

Semiclassical corrections to the interaction energy of a hard-sphere Boltzmann gas

Contact Info

Product

Resources

About