By JQL I want to know the date when the issue was assigned to a particular person
JQL is no SQL, you can't query a date, just a list of issues.
You need to capture that date in a custom field if you want to pull it into the search results. Since you are looking at the date when the issue is assigned, you will have to listen on the "Issue Assigned" event in a plugin.
Date of workflow transitions would have been easier since there are plugins that can set the current date on a custom field during workflow transitions.
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