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Long Time Deviations from the Exponential Decay Law: Possible Observational Effects

Urbanowski K., Piskorski J.

Computational Methods in Science and Technology

2010

Vol. 16, No. 2

201-205

An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable states tends to the minimal energy of the system epsilon min as t rightwards arrow infinity which is much smaller than the energy of this state for t of the order of the lifetime of the considered state. Analyzing the transition time region between the exponential and non-exponential form of the survival amplitude, we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for t from the exponential time region. Taking into account results obtained for a considered model, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as sigma meson as well as having astrophysical and cosmological consequences.

CPT and effective Hamiltonians for neutral kaon and similar complexes

Urbanowski K.

Computational Methods in Science and Technology

2005

Vol. 11, nr 1

63-71

This paper begins with a discussion of the general form and general CP- and CPT- transformation properties of the Lee-Oehme- -Yang (LOY) effective Hamiltonian for the neutral kaon complex. Next, the properties of the exact effective Hamiltonian determined by the properties of the exact transition amplitudes for this complex are discussed. Using the Khalfin Theorem we show that contrary to the standard result of the LOY theory, the diagonal matrix elements of the effective Hamiltonian governing the time evolution in the subspace of states of an unstable particle and its antiparticle need not be equal at for t > t0 (t0 is the instant of creation of the pair) when the total system under consideration is CPT invariant but CP noninvariant. The unusual consequence of this result is that, contrary to the properties of stable particles, the masses of the unstable particle “1” and its antiparticle “2” need not be equal for t o t0 in the case of preserved CPT and violated CP symmetries. We also show that there exists an approximation which is more accurate than the LOY, and which leads to an effective Hamiltonian whose diagonal matrix elements posses properties consistent with the conclusions for the exact effective Hamiltonian described above.