Quantization and conformal properties of a generalized Calogero model

Meljanac, Stjepan; Samsarov, Andjelo; Basu-Mallick, B.; Gupta, Kumar S.

doi:10.1140/epjc/s10052-006-0163-9

Cited by 23 publications

(32 citation statements)

References 62 publications

(83 reference statements)

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“…Selfadjointness of a Hamiltonian is essential, because otherwise the Hamiltonian would generate complex eigenvalues and the time evolution of the states will not be unitary. SAE has received lot of interests in recent years and is now being used extensively in different branches of physics, to explore the nontrivial quantum behavior of different systems [12,13,14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Quantization of Exciton in Magnetic Field Background

Giri

Chakrabarti

2009

Mod. Phys. Lett. A

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The possible mismatch between the theoretical and experimental absorption of the edge peaks in semiconductors in a magnetic field background may arise due to the approximation scheme used to analytically calculate the absorption coefficient. As a possible remedy we suggest to consider nontrivial boundary conditions on x-y plane by in-equivalently quantizing the exciton in background magnetic field. This inequivalent quantization is based on von Neumann's method of self-adjoint extension, which is characterized by a parameter Σ. We obtain bound state solution and scattering state solution, which in general depend upon the self-adjoint extension parameter Σ. The parameter Σ can be used to fine tune the optical absorption coefficient K(Σ) to match with the experiment.

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Section: Introductionmentioning

confidence: 99%

Quantization of Exciton in Magnetic Field Background

Giri

Chakrabarti

2009

Mod. Phys. Lett. A

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“…One possible way of constructing nontrivial boundary condition is to start with a very restricted boundary condition and then go for a possible SAE [3]. This method has been very successfully implemented in different branches of physics [3,4,5,6,7,8,9,10,11,12,13,14,15] In our present article we apply this well established method of SAE to explain the quantum dynamics of a neutral atom in the background magnetic field created by a ferromagnetic wire. Although the mathematical technicalities needed for this system is well know in the literature of mathematical physics, it is still not very frequently used especially in molecular physics.…”

Section: Introductionmentioning

confidence: 99%

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Giri

2008

Int J Theor Phys

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We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann's method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ ∈ R(mod2π). There exists a single bound state for the coupling constant η 2 ∈ [0, 1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η 2 < 0, which supports bound state making the problem re-normalizable.

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“…This is usually achieved by using von Neumann's theory [15] of self-adjoint extensions, which provides all the possible boundary conditions such that the Hamiltonian maintains self-adjointness. The theory of selfadjoint extension of the inverse square potential [16] has a long and interesting list of applications ranging from microscopic physics to black holes [17,18,19,20,21,22], and we shall apply this well established technique to explain the electron capture by polar molecules. Our approach is based on a detailed quantum mechanical treatment of the system, which suggests the possibility of the existence of bound states even though the dipole moment is less than D 0 .…”

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confidence: 99%

Electron capture and scaling anomaly in polar molecules

et al. 2008

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We present a new analysis of the electron capture mechanism in polar molecules, based on von Neumann's theory of self-adjoint extensions. Our analysis suggests that it is theoretically possible for polar molecules to form bound states with electrons, even with dipole moments smaller than the critical value D0 given by 1.63 × 10 −18 esu cm. This prediction is consistent with the observed anomalous electron scattering in H2S and HCl, whose dipole moments are smaller than the critical value D0. We also show that for a polar molecule with dipole moment less than D0, typically there is only a single bound state, which is in qualitative agreement with observations. We argue that the quantum mechanical scaling anomaly is responsible for the formation of these bound states.PACS numbers: 03.65. Ge, 31.10.+z, The experimentally observed anomalous scattering of electrons by a class of polar molecules [1,2,3] is often attributed to the electron capture by the dipole field of the polar molecules [4,5,6]. It is usually assumed that a dipole bound state of an electron is possible only if the coefficient of the inverse square interaction term is sufficiently negative, leading to a "fall to the centre" condition [7]. The point dipole model of the polar molecule predicts that the critical dipole moment [8] D 0 necessary for the electron capture has a value D 0 = 1.63 × 10 −18 esu cm [9,10,11,12], which continues to be valid for an extended dipole as well [9]. The captured electrons are usually weakly bound, which makes such bound states hard to detect unless the dipole moments are large compared to D 0 . Consequently, most of the experiments are performed with molecules having large dipole moments, for which the above value of D 0 is consistent with the experimental data.However, there are certain polar molecules, e.g. H 2 S and HCl which have dipole moments less than D 0 and yet exhibit anomalous electron scattering and can capture electrons [9,13]. The simple model of the inverse square interaction which predicts the above value of D 0 , at the first sight, seems to be inconsistent with the data for H 2 S and HCl. Moreover, the same theoretical model predicts an infinite number of bound states for dipole bound anions, whereas most experiments observe only a single bound state [14].We may think that these inconsistencies arise from the fact that the pure dipole model of a polar molecule ignores various short range interactions that play a role in the electron capture. However, the inverse square interaction between the electron and the polar molecule encodes the main aspects of the long distance dynamics leading to the formation of weakly bound states [11]. Within this approximation, and without using any detailed knowledge of the short distance interactions, it is reasonable to represent their effects through the boundary conditions obeyed by the Hamiltonian. Note that the molecular forces are usually not dissipative, and the corresponding Hamiltonian remains always self-adjoint [15]. Thus, the problem now reduces to finding al...

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Quantization and conformal properties of a generalized Calogero model

Cited by 23 publications

References 62 publications

Quantization of Exciton in Magnetic Field Background

Quantization of Exciton in Magnetic Field Background

Inequivalent Quantization in the Field of a Ferromagnetic Wire

Electron capture and scaling anomaly in polar molecules

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