WKB approximation in complex time

Biswas, S. N.; Guha, Jyotirmoy; Sarkar, N G

doi:10.1007/bf02847133

Cited by 17 publications

(26 citation statements)

References 9 publications

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“…Without going into the details of quantum vacuum, it can be said that repeated oscillation is an indication of generation of photon along with particle production. The occurrence of oscillations at Ø large negative indicate the existence of repeated reflected trajectories as is demanded in our CWKB approach [13,14,17,18]. The emergence of radiation dominated universe may thus be explained considering production and annihilation (trough and crest in figure 2e) as a mode for generation of photon at late time.…”

Section: Interpretation Of Currentsmentioning

confidence: 95%

“…For further details the reader is referred to [18], [13] and [14] to find the equivalence, If we now consider ÜÔ · Ë´Ø Ø ¼ µ as antiparticle solution, the reflected component is interpreted as a particle moving forward in time. This is the Klein paradox-like situation not in space but in time and Ê is interpreted as pair-production amplitude.…”

Section: Basic Principles Of Cwkbmentioning

confidence: 99%

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Dirac current in expanding spacetime

1999

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Section: Interpretation Of Currentsmentioning

confidence: 95%

Section: Basic Principles Of Cwkbmentioning

confidence: 99%

Dirac current in expanding spacetime

1999

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“…Many authors have considered qq pair production in the above flux tube model [4,5,[8][9][10][11][12][13][14]. The basic idea is that when two nuclei collide, they pass each other and become colour-charged, and are thus connected by colour flux tubes.…”

Section: Basic Concept Of the Problemmentioning

confidence: 99%

“…Simple geometric arguments reveal an energy density of at least εN A 1/3 GeV fm −3 . This means that an energetic collision of two 238 U nuclei provides an average deposition of approximately 6 GeV fm −3 , which is well above the level needed for plasma formation [7].Many authors have considered qq pair production in the above flux tube model [4,5,[8][9][10][11][12][13][14]. The basic idea is that when two nuclei collide, they pass each other and become colour-charged, and are thus connected by colour flux tubes.…”

mentioning

confidence: 99%

q % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVy0df9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyCayaara % aaaa!365D! $$ \bar q $$ pair production in non-Abelian gauge fields

Puzhakkal

Bannur

2007

Pramana - J Phys

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We calculate the qq pair production probability in the colour-flux tube model by considering the effect of non-Abelian interactions in the theory. Non-Abelian interactions in the colour field are time-dependent and hence should oscillate with a characteristic frequency ω 0, which depends on the amplitude of the field strength. Using the WKB approximation in complex time, we calculated the pair production probability. When the strength of the field is comparable to the quark masses, the corresponding pair creation probability is maximum, and for the static field w 0 → 0, we recovered the well-known Schwinger result. .65.-q; 25.75.-q; 25.75.Dw S M Puzhakkal and V M Bannur Basic concept of the problemWhen two nucleons collide at high energy, they almost just pass through each other. In the process, nucleons are excited, but in addition they leave a flux tube of deposited energy in the region of space they pass through. This energy is rapidly transformed into hadrons, the secondary particles usually produced in such collisions. By analysing proton-proton collision data, it is known that the deposition of energy at a higher rate is approximately 1 3 GeV fm −3 . It does not increase much more with a further increase in collision energy, which only makes the flux tube longer.If, instead of nucleons, two heavy nuclei collide (for simplicity, both with mass number A), a multiple superposition of the phenomenon just described is obtained, so that a given region of the flux tube now receives a much greater deposition of energy [6]. Simple geometric arguments reveal an energy density of at least εN A 1/3 GeV fm −3 . This means that an energetic collision of two 238 U nuclei provides an average deposition of approximately 6 GeV fm −3 , which is well above the level needed for plasma formation [7].Many authors have considered qq pair production in the above flux tube model [4,5,[8][9][10][11][12][13][14]. The basic idea is that when two nuclei collide, they pass each other and become colour-charged, and are thus connected by colour flux tubes. In these flux tubes, a strong colour electric field is set up, which makes the vacuum unstable to pair production via the Schwinger mechanism [1]. As a result, the colour field energy in the flux tube is transformed into the energy of qq pairs. Thus, in the collision process, a large number of qq pairs, together with gluons produced through interactions, ultimately leads to the formation of a QGP. The self-interaction of gluons in the flux tube is likely to polarise the medium between the two receding nuclei. This leads to a characteristic normal mode of oscillations. Therefore, the colour field in the flux tube should be time-dependent (colour particles are coupled to each other via the gauge fields). These collective oscillations are non-Abelian. Hence, we assume a non-Abelian colour field model in which the characteristic frequency of collective oscillation depends on the amplitude of the oscillation.During a nucleus-nucleus collision, a QGP is formed at the centre of the tube, which ...

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“…In this case, there are variant results in the literature. We test it through the CWKB (complex trajectory WKB) method developed by Biswas et al [1][2][3][4][5] by calculating the envelope and finding whether it fits correctly over the occupation number. The envelope is the curve joining the maximum of occupation number (N k ) vs. k. The standard approach is to calculate N k using Runge-Kutta IV method and the envelope is calculated using the technique given in [6] and subsequently used by Greene and Kofman [7,8].…”

Section: Introductionmentioning

confidence: 99%

Calculation of CWKB envelope in boson and fermion productions

Biswas

Chowdhury

2007

Pramana - J Phys

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We present the calculation of envelope of boson and of both low-and highmass fermion production at the end of inflation when the coherently oscillating inflatons decay into bosons and fermions. We consider three different models of inflation and use CWKB technique to calculate the envelope to understand the structure of resonance band formation. We observe that though low-mass fermion production is not effective in preheating because of Pauli blocking, it is quite probable for high-mass fermion to take part in pre-heating.

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WKB approximation in complex time

Cited by 17 publications

References 9 publications

Dirac current in expanding spacetime

Dirac current in expanding spacetime

Calculation of CWKB envelope in boson and fermion productions

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